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Math Review Convert the following numbers to scientific notation. (a) 568 017 (b) 0.000 309Math Review Simplify the following expression in terms of the dimensions mass, length, and time given by [M], [L],and [T]. (See Section 1.3.) [M][L]2[T]3[T][L][T]=?Simplify the following expression, combining terms as appropriate and combining and canceling units. (See Section 1.5.) (7.00ms2)(1.00km1.00103m)(60.0s1.00min)z=?The Roman cubitus is an ancient unit of measure equivalent to about 0.445 m. Convert the 2.00-m height of a basketball forward to cubiti. (See Section 1.5.)A house is advertised as having 1 420 square feet under roof. What is the area of this house in square meters? (Sec Section 1.5.)A rectangular airstrip measures 32.30 m by 210 m, with the width measured more accurately than the length. Find the area, taking into account significant figures. (See Section 1.4.)Use the rules for significant figures to find the answer to the addition problem 21.4 + 15 + 17.17 + 4.003. (See Section 1.4).Find the polar coordinates corresponding to a point located at (5.00, 12.00) in Cartesian coordinates. (See Section 1.7.)9WUEEstimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b) a pool cue, (c) a basketball court, (d) an elephant, (e) a city block.What types of natural phenomena could serve as time standards?Find the order of magnitude of your age in seconds.An object with a mass of 1 kg weighs approximately 2 lb. Use this information to estimate the mass of the following objects: (a) a baseball, (b) your physics textbook, (c) a pickup truck.(a) Estimate the number of times your heart beats in a month, (b) Estimate the number of human heartbeats in an average lifetime.Estimate the number of atoms in 1 cm5 of a solid. (Note that the diameter of an atom is about 1010 m.)The height of a horse is sometimes given in units of hands. Why is this a poor standard of length?9CQWhy is the metric system of units considered superior to most other systems of units?How can an estimate be of value even when it is off by on order of magnitude? Explain and give an example.Suppose two quantities, A and B, have different dimensions. Determine which of the following arithmetic operations could be physically meaningful, (a) A + B (b) B A (c) A B (d) A/B (e) ABAnswer each question yes or no. Must two quantities have the same dimensions (a) if you are adding them? (b) If you are multiplying them? (c) If you are subtracting them? (d) If you are dividing them? (e) If you are equating them?The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T=2lg where is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent. (You might want to check the formula using your keys at the end of a string and a stopwatch.)(a) Suppose the displacement of an object is related to time according to the expression x = Bt2. What are the dimensions of B? (b) A displacement is related to time as x = A sin (2ft), where A and f are constants. Find the dimensions of A. Hint: A trigonometric function appearing in an equation must be dimensionless.A shape that covers an area A and has a uniform height h has a volume V = Ah. (a) Show that V = Ah is dimensionally correct. (b) Show that the volumes of a cylinder and of a rectangular box can be written in the form V = Ah, identifying A in each case. (Note that A, sometimes called the footprint of the object can have any shape and that the height can, in general, be replaced by the average thickness of the object.)Each of the following equations was given by a student during an examination: (a) 12mv2=12mv02+mgh (b) v = v0 + at2 (c) ma = v2. Do a dimensional analysis of each equation and explain why the equation cant be correct.5PKinetic energy KE (Topic 5) has dimensions kg m2/s2. It can be written in terms of the momentum p (Topic 6) and mass m as KE=p22m (a) Determine the proper units for momentum using dimensional analysis. (b) Refer to Problem 5. Given the units of force, write a simple equation relating a constant force F exerted on an object, an interval of time t during which the force is applied, and the resulting momentum of the object, p.A carpet is to be installed in a room of length 9.72 m and width 5.3 m. Find the area of the mom retaining the proper number of significant figures.8PHow many significant figures are there in (a) 78.9 0.2, (b) 3.788 109, (c) 2.46 1026, (d) 0.003 2The speed of light is now defined to be 2.997 924 58 108 m/s. Express the speed of light to (a) three significant figures, (b) five significant figures, and (c) seven significant figures.A block of gold has length 5.62 cm. width 6.35 cm, and height 2.78 cm. (a) Calculate the length times the width and round the answer to the appropriate number of significant figures. (b) Now multiply the rounded result of part (a) by the height and again round, obtaining the volume. (c) Repeat the process, first finding the width limes the height, founding it, and then obtaining the volume by multiplying by the length. (d) Explain why the answers dont agree in the third significant figure.The radius of a circle is measured to be (10.5 0.2) m. Calculate (a) the area and (b) the circumference of the circle, and give the uncertainty in each value.The edges of a shoebox are measured to be 11.4 cm, 17.8 cm, and 29 cm. Determine the volume of the box retaining the proper number of significant figures in your answer.Carry out the following arithmetic operations: (a) the sum of the measured values 756, 37.2, 0.83, and 2.5; (b) the product 0.003 2 356.3; (c) the product 5.620 .A fathom is a unit of length, usually reserved for measuring the depth of water. A fathom is approximately 6 ft in length. Take the distance from Earth to the Moon to be 250 000 miles, and use the given approximation to find the distance in fathoms.A small turtle moves at a speed of 186 furlongs per fortnight. Find the speed of the turtle in centimeters per second. Note that 1 furlong = 220 yards and 1 fortnight = 14 days.A firkin is an old British unit of volume equal to 9 gallons. How many cubic meters are there in 6.00 firkins?Find the height or length of these natural wonders in kilometers, meters, and centimeters: (a) The longest cave system in the world is the Mammoth Cave system in Central Kentucky, with a mapped length of 348 miles, (b) In the United States, the waterfall with the greatest single drop is Ribbon Falls in California, which drops 1 612 ft. (c) At 20 320 feet, Mount McKinley in Alaska is America's highest mountain, (d) The deepest canyon in the United States is Kings Canyon in California, with a depth of 8 200 ft.A car is traveling at a speed of 38.0 m/s on an interstate high-way where the speed limit is 75.0 mi/h. Is the driver exceeding the speed limit? Justify your answer.A certain car has a fuel efficiency of 25.0 miles per gallon (mi/gal). Express this efficiency in kilometers per liter (km/L).The diameter of a sphere is measured to be 5.36 in. Find (a) the radius of the sphere in centimeters, (b) the surface area of the sphere in square centimeters, and (c) the volume of the sphere in cubic centimeters.Suppose your hair grows at the rate of 1/32 inch per day. Find the rate at which it grows in nanometers per second. Because the distance between atoms in a molecule is on the order of 0.1 nm, your answer suggests how rapidly atoms are assembled in this protein synthesis.The speed of light is about 3.00 108 m/s. Convert this figure to miles per hour.A house is 50.0 ft long and 26 ft wide and has 8.0-ft-high ceilings. What is the volume of the interior of the house in cubic meters and in cubic centimeters?The amount of water in reservoirs is often measured in acre-ft. One acre-ft is a volume that covers an area of one acre to a depth of one foot An acre is 43 560 ft2. Find the volume in SI units of a reservoir containing 25.0 acre-ft of water.The base of a pyramid covers an area of 13.0 acres (1 acre = 43 560 ft2) and has a height of 481 ft (Fig. P1.30). If the volume of a pyramid is given by the expression V = bh/3, where b is the area of the base and h is the height, find the volume of this pyramid in cubic meters. Figure P1.30A quart container of ice cream is to be made in the form of a cube. What should be the length of a side, in centimeters? (Use the conversion 1 gallon = 3.786 liter.)Estimate the number of steps you would have to take to walk a distance equal to the circumference of the Earth.Estimate the number of breaths taken by a human being during an average lifetime.Estimate the number of people in the world who are suffering from the common cold on any given day. (Answers may vary. Remember that a person suffers from a cold for about a week.)(a) About how many microorganisms are found in the human intestinal tract? (A typical bacterial length scale is one micron = 106 m. Estimate the intestinal volume and assume bacteria occupy one hundredth of it.) (b) Discuss your answer to part (a). Are these bacteria beneficial, dangerous, or neutral? What functions could they serve?Treat a cell in a human as a sphere of radius 1.0 m. (a) Determine the volume of a cell. (b) Estimate the volume of your body. (c) Estimate the number of cells in your body.An automobile tire is rated to last for 50 000 miles. Estimate the number of revolutions the tire will make in its lifetime.Bacteria and other prokaryotes are found deep underground, in water, and in the air. One micron (106 m) is a typical length scale associated with these microbes. (a) Estimate the total number of bacteria and other prokaryotes in the biosphere of the Earth. (b) Estimate the total mass of all such microbes. (c) Discuss the relative importance of humans and microbes to the ecology of planet Earth. Can Homo sapiens survive without them?A point is located in a polar coordinate system by the coordinates r = 2.5 m and = 35. Find the x- and y-coordinates of this point, assuming that the two coordinate systems have the same origin.A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (2.0, 1.0), where the units are meters, what is the distance of the fly from the corner of the room?Express the location of the fly in Problem 40 in polar coordinates.Two points in a rectangular coordinate system have the coordinates (5.0, 3.0) and (3.0, 4.0), where the units are centimeters. Determine the distance between these points.Two points are given in polar coordinates by (r, ) = (2.00 m, 50.0) and (r, ) = (5.00 m, 50.0), respectively. What is the distance between them?Given points (r1, 1) and (r2, 2) in polar coordinates, obtain a general formula for the distance between them. Simplify it as much as possible using the identity cos2 + sin2 = 1. Hint: Write the expressions for the two points in Cartesian coordinates and substitute into the usual distance formula.For the triangle shown in Figure P1.45, what are (a) the length of the unknown side, (b) the tangent of , and (c) the sine of ? Figure P1.45A ladder 9.00 m long leans against the side of a building. If the ladder is inclined at an angle of 75.0 to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?A high fountain of water is located at the center of a circular pool as shown in Figure P1.47. Not wishing to get his feet wet, a student walks around the pool and measures its circumference to be 15.0 m. Next, the student stands at the edge of the pool and uses a protractor to gauge the angle of elevation at the bottom of the fountain to be 55.0. How high is the fountain? Figure P1.47A right triangle has a hypotenuse of length 3.00 m, and one of its angles is 30.0. What are the lengths of (a) the side opposite the 30.0 angle and (b) the side adjacent to the 30.0 angle?In Figure P1.49, find (a) the side opposite , (b) the side adjacent to . (c) cos , (d) sin , and (c) tan . Figure P1.49In a certain right triangle, the two sides that are perpendicular to each other are 5.00 m and 7.00 m long. What is the length of the third side of the triangle?In Problem 50, what is the tangent of the angle for which 5.00 in is the opposite side?48PA surveyor measures the distance across a straight river by the following method: starting directly across from a tree on the opposite bank, he walks x = 1.00 102 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline lo the tree is = 35.0 (Fig. P1.53). How wide is the river? Figure P1.5350P(a) One of lire fundamental laws of motion states that the acceleration of an object is directly proportional to the resultant force on it and inversely proportional to its mass. If the proportionality constant is defined to have no dimensions, determine the dimensions of force. (b) The newton is the SI unit of force. According to the results for (a), how can you express a force having units of newtons by using the fundamental units of mass, length, and time?(a) Find a conversion factor to convert from miles per hour to kilometers per hour. (b) For a while, federal law mandated that the maximum highway speed would be 55 mi/h. Use the conversion factor from part (a) to find the speed in kilometers per hour. (c) The maximum highway speed has been raised to 65 mi/h in some places. In kilometers per hour, how much of an increase is this over the 55-mi/h limit?One cubic centimeter (10 cm3) of water has a mass of 1.0 103 kg. (a) Determine the mass of 1.0 m3 of water. Assuming that biological substances are 98% water, estimate the masses of (b) a cell with a diameter of 10 m, (c) a human kidney, and (d) a fly Take a kidney to be roughly a sphere with a radius of 4.0 cm and a fir to be roughly a cylinder 4.0 mm long and 2.0 mm in diameter.54APThe displacement of an object moving under uniform acceleration is some function of time and the acceleration. Suppose we write this displacement as s = kamtn, where k is a dimensionless constant Show by dimensional analysis that this expression is satisfied if m = 1 and n = 2. Can the analysis give the value of k?Assume it takes 7.00 minutes to fill a 30.0-gal gasoline tank. (a) Calculate the rate at which the tank is filled in gallons per second. (b) Calculate the rate at which the tank is filled in cubic meters per second. (c) Determine the time interval, in hours, required to fill a 1.00-m3 volume at the same rate. (1 U.S. gal = 231 in.3)One gallon of paint (volume = 3.79 103 m3) covers an area of 25.0 m2. What is the thickness of the fresh paint on the wall?A sphere of radius r has surface area A = 4r2 and volume V = (4/3)r3. If the radius of sphere 2 is double the radius of sphere 1, what is the ratio of (a) the areas, A2/A1 and (b) the volumes, V2/V1?Assume there are 100 million passenger can in the United States and that the average fuel consumption is 20 mi/gal of gasoline. If the average distance traveled by each car is 10 000 mi/yr, how much gasoline would be saved per year if average fuel consumption could be increased to 25 mi/gal?60AP(a) How many seconds are there in a year? (b) If one micrometeorite (a sphere with a diameter on the order of 106 m) struck each square meter of the Moon each second, estimate the number of years it would take to cover the Moon with micrometeorites to a depth of one meter. (Hint: Consider a cubic box, 1 m on aside, on the Moon, and find how long it would take to fill the box.)Imagine that you are the equipment manager of a professional baseball team. One of your jobs is to keep baseballs on hand for games. Balls are sometimes lost when players hit them into the stands as either home runs or foul balls. Estimate how many baseballs you have to buy per season in order to make up for such losses. Assume that your team plays an 81-game home schedule in a season.The nearest neutron star (a collated star made primarily of neutrons) is about 3.00 1018 m away from Earth. Given that the Milky Way galaxy (Fig. P1.81) is roughly a disk of diameter 1021 m and thickness 1019 m, estimate the number of neutron stars in the Milky Way to the nearest order of magnitude. Figure P1.81Figure 2.4 shows the unusual path of a confused football player. After receiving a kickoff at his own goal, he runs downfield to within inches of a touchdown, then reverses direction and races back until hes tackled at the exact location where he first caught the ball. During this run, which took 25 s, what is (a) the path length he travels, (b) his displacement, (c) his average velocity in the x-direction, and (d) his average speed? Figure 2.4 (Quick Quiz 2.1) The path followed by a confused football player.True or False? (a) A car must always have an acceleration in the same direction as its velocity. (b) Its possible for a slowing car to have a positive acceleration. (c) An object with constant nonzero acceleration can never stop and remain at rest.Parts (a), (b), and (c) of Figure 2.10 represent three graphs of the velocities of different objects moving in straight-line paths as functions of time. The possible accelerations of each object as functions of time are shown in parts (d), (c), and (f). Match each velocity vs. time graph with the acceleration vs. time graph that best describes the motion. Figure 2.10 (Quick Quiz 2.3) Match each velocity vs. time graph to its corresponding acceleration vs. time graph.The three graphs in Figure 2.13 represent the position vs. time for objects moving along the x-axis. Which, if any, of these graphs is not physically possible? Figure 2.13 (Quick Quiz 2.4) Which position vs. time curve is impossible?Figure 2.14a is a diagram of a multiflash image of an air puck moving to the right on a horizontal surface. The images sketched are separated by equal time intervals, and the first and last images show the puck al rest. (a) In Figure 2.14b, which color graph best shorn the pucks position as a function of time? (b) In Figure 2.14c, which color graph best shows the pucks velocity as a function of time? (c) In Figure 2.l4d, which color graph best shows the puck's acceleration as a function of time? Figure 2.14 (Quick Quiz 2.5) Choose the correct graphs.A tennis player on serve tosses a ball straight up. While the ball is in free fall, does its acceleration (a) increase, (b) decrease, (c) increase and then decrease, (d) decrease and then increase, or (e) remain constant?As the tennis ball of Quick Quiz 2.6 travels through the air, does its speed (a) increase, (b) decrease, (c) decrease and then increase, (d) increase and then decrease, or (c) remain the same?A skydiver jumps out of a hovering helicopter. A few seconds later, another skydiver jumps out, so they both fall along the same vertical line relative to the helicopter. Assume both skydivers fall with the same acceleration. Does the vertical distance between them (a) increase, (b) decrease, or (c) stay the same? Does the difference in their velocities (d) increase, (e) decrease, or (f) stay the same?Math Review Solve the quadratic equation 2.00t2 6 00t 9.00 = 0 using the quadratic formula, finding both solutions.Math Review Solve the following two equations for (a) the time t, and (b) the position, x. Assume SI units. 9.8t + 49 = 0 and x = 4.9t2 + 49t + 16Math Review Solve the following two equations for (a) the (positive) time t, and (b) the position x. Assume SI units. x = 3.00t2 x= 24.0t + 72.0A football player runs from his own goal line to the opposing teams goal line, returning to the fifty-yard line, all in 18.0 s. Calculate (a) his average speed, and (b) the magnitude of his average velocity. (Sec Section 2.2)A ball is thrown downward from the top of a 40.0 m tower with an initial speed of 12.0 m/s. Assuming negligible air resistance, what is the speed of the ball just before hitting the ground? (See Section 2.6.)An arrow is shot straight up in the air at an initial speed of 15.0 m/s. After how much time is the arrow heading downward at a speed of 8.00 m/s? (See Section 2.6.)A red ball is dropped from rest at a height of 6.00 m. A blue ball at a height of 10.0 m is thrown down at the same instant at 4.00 m/s. How long does it take the blue ball to catch up with the red ball? (See Sections 2.5 and 2.6.)If the velocity of a particle is nonzero, can the particles acceleration be zero? Explain.If the velocity of a particle is zero, can the particles acceleration be nonzero? Explain.If a car is traveling eastward, can its acceleration be westward? Explain.(a) Can the equations in Table 2.4 be used in a situation where the acceleration varies with time? (b) Can they be used when the acceleration is zero? Table 2.4 Equations for Motion in a Straight Line Under Constant Acceleration Equation Information Given by Equation v = v0 + at velocity as a function of time x = v0t + 12at2 Displacement as a function of time v2 = v02 + 2ax Velocity as a function if displacement Note: Motion is along the x -axis. At t = 0, the velocity of the particle is vTwo cars are moving in the same direction in parallel lanes along a highway. At some instant, the velocity of car A exceeds the velocity of car B. Does that mean that the acceleration of A is greater than that of B at that instant? Explain.Figure CQ2.6 shows strobe photographs taken of a disk moving from left to right under different conditions. The time interval between images is constant. Taking the direction to the right, to be positive, describe the motion of the disk in each case. For which case is (a) the acceleration positive? (b) the acceleration negative? (c) the velocity constant? Figure CQ2.6(a) Can the instantaneous velocity of an object at an instant of time ever be greater in magnitude than the average velocity over a lime interval containing that instant? (b) Can it ever be less?A ball is thrown vertically upward. (a) What are its velocity and acceleration when it reaches its maximum altitude? (b) What is the acceleration of the ball just before it hits the ground?Consider the following combinations of signs and values for the velocity and acceleration of a particle with respect to a one-dimensional x-axis: Velocity Acceleration a. Positive Positive b. Positive Negative c. Positive Zero d. Negative Positive e. Negative Negative f. Negative Zero g. Zero Positive h. Zero Negative Describe what the particle is doing in each case and give a real-life example for an automobile on an east-west one-dimensional axis, with east considered the positive direction.A ball rolls in a straight line along the horizontal direction. Using motion diagrams (or multi flash photo-graphs), describe the velocity and acceleration of the ball for each of the following situations: (a) The ball moves to the right at a constant speed, (b) The ball moves from right to left and continually slows down, (c) The ball moves from right to left and continually speeds up. (d) The ball moves to the right, first speeding up at a constant rate and then slowing down at a constant rate.An object moves along the x-axis, its position given by x(t) = 2t2. Which of the following cannot be obtained from a graph of x vs. t? (a) The velocity at any instant (b) the acceleration at any instant (c) the displacement during some time interval (d) the average velocity during some time interval (e) the speed of the particle at any instant.A ball is thrown straight up in the air. For which situation are both the instantaneous velocity and the acceleration zero? (a) On the way up (b) at the top of the flight path (c) on the way down (d) half-way up and halfway down (e) none of these.A juggler throws a bowling pin straight up in the air. After the pin leaves his hand and while it is in the air, which statement is true? (a) The velocity of the pin is always in the same direction as its acceleration. (b) The velocity of the pin is never in the same direction as its acceleration. (c) The acceleration of the pin is zero. (d) The velocity of the pin is opposite its acceleration on the way up. (e) The velocity of the pin is in the same direction as its acceleration on the way up.A racing car starts from rest and reaches a final speed v in a time t. If the acceleration of the car is constant during this time, which of the following statements must be true? (a) The car travels a distance vt. (b) The average speed of the car is v/2. (c) The acceleration of the car is v/t. (d) The velocity of the car remains constant. (e) None of these.The speed of a nerve impulse in the human body is about 100 m/s. If you accidentally stub your toe in the dark, estimate the time it takes the nerve impulse to your brain.Light travels at a speed of about 3 103 m/s. (a) How many miles down a pulse of light travel in a time interval of 0.1 s, which is about the blink of an eye? (b) Compare this distance to the diameter of Earth.A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30.0 min at 80.0 km/h, 12.0 min at 100 km/h, and 45.0 min at 40.0 km/h and spends 15.0 min eating lunch and buying gas. (a) Determine the average speed for the trip. (b) Determine the distance between the initial and final cities along the route.The current indoor world record time in the 200-m race is 19.92 s, held by Frank. Fredericks of Namibia (1996), while the indoor record time in the one-mile race is 228.5 s, held by Hicham El Guerrouj of Morroco (1997). Find the mean speed in meters per second corresponding to these record times for (a) the 200-m event and (b) the one-mile event.Two boats start together and race across a 60-km-wide lake and back. Boat A goes across at 60 km/h and returns at 60 km/h. Boat B goes across at 30 km/h, and its crew, realizing how far behind it is getting, returns at 90 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins. (a) Which boat wins and by how much? (Or is it a tie?) (b) What is the average velocity of the winning boat?A graph of position versus time for a certain particle moving along the x-axis is shown in Figure P2.6. Find the average velocity in the time intervals from (a) 0 to 2.00 s, (b) 0 to 4.00 s, (c) 2.00 s to 4.00 s, (d) 4.00 s to 7.00 s, and (e) 0 to 8.00 s. Figure P2.6 (Problems 6 and 17)A motorist drives for 35.0 minutes at 85.0 km/h and then stops for 15.0 minutes. He then continues north, traveling 130. Km in 2.00 h. (a) What is his total displacement? (b) What is his average velocity?A tennis player moves in a straight-line path as shown in Figure P2.8. Find her average velocity in the time intervals from (a) 0 to 1.0 s, (b) 0 to 4.0 s, (c) 1.0 s to 3.0 s, and (d) 0 to 5.0 s. Figure P2.8A jet plane has a takeoff speed of v0 = 75 m/s and can move along the runway at an average acceleration of 1.3m/s2. If the length of the runway is 2.5 km, will the plane be able to use this runway safely? Defend your answer.Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/h. (a) Assuming they start at the same point, how much sooner does the faster car arrive at a destination 10 mi away? (b) How far must the faster car travel before it has a 15-min lead on the slower car?The cheetah can reach a top speed of 114 km/h (71 mi/h). While chasing its prey in a short sprint, a cheetah starts from rest and runs 45 m in a straight line, reaching a final speed of 72 km/h. (a) Determine the cheetahs average acceleration during the short sprint, and (b) find its displacement at t = 3.5 s.An athlete swims the length L of a pool in a time t1 and makes the return trip to the starting position in a time t2. If she is swimming initially in the positive x-direction, determine her average velocities symbolically in (a) the first half of the swim, (b) the second half of the swim, and (c) the round trip, (d) What is her average speed for the round trip?A person lakes a trip, driving with a constant speed of 89.5 km/h, except, for a 22.0-min rest stop. If the persons average speed is 77.8 km/h, (a) how much time is spent on the trip and (b) how far does the person travel?A tortoise can run with a speed of 0.10 m/s, and a hare can run 20 times as fast. In a race, they both start at the same time, but the hare stops to rest for 2.0 minutes. The tortoise wins by a shell (20 cm). (a) How long does the race take? (b) What is the length of the race?To qualify for the finals in a racing event, a race car must achieve an average speed of 250. km/h on a track with a total length of 1.60 103. If a particular car covers the first half of the track at an average speed of 230. km/h, what minimum average speed must it have in the second half of the event to qualify?16PA graph of position versus time for a certain particle moving along the x-axis is shown in Figure P2.6. Find the instantaneous velocity at the instants (a) t = 1.00 s, (b) t = 3.00 s, (c) t = 4.50 s, and (d) t = 7.50 s.A race car moves such that, its position fits the relationship x = (5.0 m/s)t + (0.75 m/s3)t3 where x is measured in meters and t in seconds. (a) Plot a graph of the car's position versus time. (b) Determine the instantaneous velocity of the car at t = 4.0 s, using time intervals of 0.40 s, 0.20 s, and 0.10 s. (c) Compare the average velocity during the first 4.0 s with the results of part (b).Runner A is initially 4.0 mi west of a flagpole and is running with a constant velocity of 6.0 mi/h due east. Runner B is initially 3.0 mi east of the flagpole and is running with a constant velocity of 5.0 mi/h due west. How far are the runners from the flagpole when they meet?A particle starts from rest and accelerates as shown in Figure P2.20. Determine (a) the particles speed at t = 10.0 s and at t = 20.0 s, and (b) the distance traveled in the first 20.0 s. Figure P2.20A 50.0-g Super Ball traveling at 25.0 m/s bounces off a brick will and rebounds at 22.0 m/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.50 ms, what is the magnitude of the average acceleration of the ball during this time interval?The average person passes out at an acceleration of 7g (that is, seven times the gravitational acceleration on Earth). Suppose a car is designed to accelerate at this rate. How much time would be required for the car to accelerate from rest, to 60.0 miles per hour? (The car would need rocket boosters!)A certain car is capable of accelerating at a rate of 0.60 m/s2. How long does it take for this car to go from a speed of 55 mi/h to a speed of 60 mi/h?The velocity vs. time graph for an object moving along a straight path is shown in Figure P2.21. (i) Find the average acceleration of the object during the time intervals (a) 0 to 5.0 s, (b) 5.0 s to 15 s. and (c) 0 to 20 s. (ii) Find the instantaneous acceleration at (a) 2.0 s, (b) 10 s, and (c) 18 s. Figure P2.24A steam catapult launches a jet aircraft from the aircraft carrier John C. Stennis, giving it a speed of 175 mi/h in 2.50 s. (a) Find the average acceleration of the plane. (b) Assuming the acceleration is constant, find the distance the plane moves.PROBLEM A race car starting from rest accelerates at a constant rate of 5.00 m/s2, (a) What is the velocity of the car after it has traveled 1.00 102 ft? (b) How much time has elapsed? (c) Calculate the average velocity two different ways. STRATEGY Weve read the problem, drawn the diagram in Figure 2.16, and chosen a coordinate system (steps 1 and 2). We'd like to find the velocity v after a certain known displacement x. The acceleration a is also known, as is the initial velocity v0 (step 3, labeling, is complete), so the third equation in Table 2.4 looks most useful for solving part (a). Given the velocity, the first equation in Table 2.4 can then be used to find the time in part (b). Part (c) requires substitution into Equations 2.2 and 2.7, respectively. Figure 2.16 (Example 2.4) SOLUTION (a) Convert units of x to SI, using the information in the inside front cover. Write the kinematics equation for v2 (step 4): Solve for v, taking the positive square root because the car moves to the right (step 5): Substitute v0 = 0, a = 5.00 m/s2, and x = 30.5 m: 1.00 102ft = (1.00 102 ft) v2 = v02 + 2a x v = v02+2ax v = v02+2ax = (0)2+2(5.00m/s2)(30.5m)= 17.5 m/s (b) Find the trooper's speed at that time. Substitute the time into the troopers velocity equation: vtrooper = v0 + atrooper t = 0 + (3.00m/s2)(16.9s) = 50.7 m/s Solve Example 2.5, Car Chase, by a graphical method. On the same graph, plot position versus time for the car and the trooper. From the intersection of the two curves, read the time at which the trooper overtakes the car.An object moving with uniform acceleration has a velocity of 12.0 cm/s in the positive x-direction when its x-coordinate is 3.00 cm. If its x-coordinate 2-00 s later is 5.00 cm, what is its acceleration?In 1865 Jules Verne proposed sending men to the Moon by firing a space capsule from a 220-m-long cannon with final speed of 10.97 km/s. What would have been the unrealistically large acceleration experienced by the space travelers during their launch? (A human can stand an acceleration of 15g for a short time.) Compare your answer with the free-fall acceleration, 9.80 m/s2.A truck covers 40.0 m in 8.50 s while uniformly slowing down to a final velocity of 2.80 m/s. (a) Find the trucks original speed. (b) Find its acceleration.A speedboat increases its speed uniformly from vi = 20.0 m/s to Vf = 30.0 m/s in a distance of 2.00 102 m. (a) Draw a coordinate system for this situation and label the relevant quantities, including vectors, (b) For the given information, what single equation is most appropriate for finding the acceleration? (c) Solve the equation selected in part (b) symbolically for the boats acceleration in terms of vf, vi, and x. (d) Substitute given values, obtaining that acceleration, (e) Find the time it takes the boat to travel the given distance.A Cessna aircraft has a liftoff speed of 120. km/h. (a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 240. m? (b) How long does it take the aircraft to become airborne?An object moves with constant acceleration 4.00 m/s2 and over a time interval reaches a final velocity of 12.0 m/s. (a) If its original velocity is 6.00m/s, what is its displacement during the time interval? (b) What is the distance it travels during this interval? (c) If its original velocity is 6.00 m/s, what is its displacement during this interval? (d) What is the total distance it travels during the interval in part (c)?In a test run, a certain car accelerates uniformly from zero to 24.0 m/s in 2.95 s. (a) What is the magnitude of the cars acceleration? (b) How long does it take the car to change its speed from 10.0 m/s to 20.0 m/s? (c) Will doubling the time always double the change in speed? Why?A jet plane lands with a speed of 100 m/s and can accelerate at a maximum rate of 5.00 m/s2 as it comes to rest. (a) From the instant the plane touches the runway, what is the minimum time needed before it can come to rest? (b) Can this plane land on a small tropical island airport where the runway is 0.800 km long?Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 155 m ahead traveling at 5.00 m/s. Sue applies her brakes but can accelerate only at 2.00 m/s2 because the road is wet. Will there be a collision? State how you decide. If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sues car and the van.A record of travel along a straight path is as follows: 1. Start from rest with a constant acceleration of 2.77 m/s2 for 15.0 s. 2. Maintain a constant velocity for the next. 2.05 min. 3. Apply a constant negative acceleration of 9.47 m/s2 for 4.39 s. (a) What was the total displacement for the trip? (b) What were the average speeds for legs 1, 2, and 3 of the trip, as well as for the complete trip? trip, as well as for the complete trip?A train is traveling down a straight track at 20 m/s when the engineer applies the brakes, resulting in an acceleration of 1.0 m/s2 as long as the train is in motion. How far does the train move during a 40-s time interval starting at the instant the brakes are applied?A car accelerates uniformly from rest to a speed of 40.0 mi/h in 12.0 s. Find (a) the distance the car travels during this time and (b) the constant acceleration of the car.A car starts from rest and travels for 5.0 s with a uniform acceleration of +1.5 m/s2. The driver then applies the brakes, causing a uniform acceleration of 2.0 m/s2. If the brakes are applied for 3.0 s, (a) how fast is the car going at the end of the braking period, and (b) how far has the car gone?A car starts from rest and travels for t1 seconds with a uniform acceleration a1. The driver then applies the brakes, causing a uniform acceleration a2. If the brakes are applied for t2 seconds, (a) how fast is the car going just, before the beginning of the braking period? (b) How far does the car go before the driver begins to brake? (c) Using the answers to parts (a) and (b) as the initial velocity and position for the motion of the car during braking, what total distance does the car travel? Answers are in terms of the variables a1, a2, t1, and t2.In the Daytona 500 auto race, a Ford Thunderbird and a Mercedes Benz are moving side by side down a straightaway at 71.5 m/s. The driver of the Thunderbird realizes that she must make a pit stop, and she smoothly slows to a stop over a distance of 250 in. She spends 5.00 s in the pit and then accelerates out, reaching her previous speed of 71.5 m/s after a distance of 350 m. At this point, how far has the Thunderbird fallen behind the Mercedes Benz, which has continued at a constant speed?A certain cable car in San Francisco can stop in 10 % when traveling at maximum speed. On one occasion, the driver seen a dog a distance d in front of the car and slams on the brakes instantly. The car reaches the dog 8.0 s later, and the dog jumps off the track just in time. If the car travels 4.0 m beyond the position of the dog before coming to a stop, how far was the car from the dog? (Hint: You will need three equations.)A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 12 m/s, skates by with the puck. After 3.0 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 4.0 m/s2, (a) how long does it take him to catch his opponent, and (b) how far has he traveled in dial time? (Assume the player with the puck remains in motion al constant speed.)A train 4.00 102 m long is moving on a straight track with a speed of 82.4 km/h. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 16.4 km/h. Assuming constant acceleration, determine how long the train blocked the crossing. Disregard the width of the crossing.A ball is thrown vertically upward with a speed of 25.0 m/s. (a) How high does it rise? (b) How long does it take to reach its highest point? (c) How long does the ball take to hit the ground after it reaches its highest point? (d) What is its velocity when it returns to the level from which it started?A ball is thrown directly downward with an initial speed of 8.00 m/s, from a height of 30.0 m. After what time interval does it strike the ground?A certain freely falling object, released from rest, requires 1.50 s to travel the last 30.0 m before it hits the ground. (a) Find the velocity of the object when it is 30.0 m above the ground. (b) Find the total distance the object travels during the fall.An attacker at the base of a castle wall 3.65 m high throws a rock straight up with speed 7.40 m/s at a height of 1.55 m above the ground, (a) Will the rock reach the top of the wall? (b) If so, what is the rock's speed at the top? If not, what initial speed must the rock have to reach the top? (c) Find the change in the speed of a rock thrown straight down from the top of the wall at an initial speed of 7.40 m/s and moving between the same two points, (d) Does the change in speed of the downward-moving rock agree with the magnitude of the speed change of the rock moving upward between the same elevations? Explain physically why or why not.Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1 000 m/s2 lasting tor at least 1 ms will cause injury. Suppose; a small child rolls off a bed that is 0.40 m above the floor. If the floor is hardwood, the childs head is brought to rest in approximately 2.0 min. If the floor is carpeted, this stopping distance is increased to about 1.0 cm. Calculate the magnitude and duration of the deceleration. In both cases, to determine the risk of injury. Assume the child remains horizontal during the fall to the floor. Note that a more complicated fall could result in a head velocity greater or less than the speed you calculate.A small mailbag is released from a helicopter that is descending steadily at 1.50 m/s. After 2.00 s, (a) what is the speed of the mailbag, and (b) how far is it below the helicopter? (c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at 1.50 m/s?A tennis player tosses a tennis ball straight up and then catches it after 2.00 s at the same height as the point of release. (a) What is the acceleration of the ball while it is in flight? (b) What, is the velocity of the ball when it reaches its maximum height? Find (c) the initial velocity of the ball and (d) the maximum height it reaches.A package is dropped from a helicopter that is descending steadily at a speed vn. After t seconds have elapsed, (a) what is the speed of the package in terms of vn, g, and t? (b) What distance d is it from the helicopter in terms of g and t? (c) What are the answers to parts (a) and (b) if the helicopter is rising steadily at the same speed?A model rocket is launched straight upward with an initial speed of 50.0 m/s. It accelerates with a constant upward acceleration of 2.00 m/s2 until its engines stop at an altitude of 150. m. (a) What can you say about, the motion of the rocket alter its engines stop? (b) What is the maximum height reached by the rocket? (c) How long after liftoff does the rocket reach its maximum height? (d) How long is the rocket in the air?A baseball is hit so that it travels straight upward after being struck by the bat. A fan observes that it takes 3.00 s for the ball to reach its maximum height. Find (a) the balls initial velocity and (b) the height it reaches.A truck tractor pulls two trailers, one behind the other, at a constant speed of 1.00 102 km/h. It takes 0.600 s for the big rig to completely pass onto a bridge 4.00 102 m long. For what duration of time is all or part of the truck-trailer combination on the bridge?Colonel John P. Stapp, USAF, participated in studying whether a jet pilot could survive emergency ejection. On March 19, 1954, he rode a rocket-propelled sled that moved down a track at a speed of 632 mi/h (see Fig. P2.56). He and the sled were safely brought to rest in 1.40 s. Determine in SI units (a) the negative; acceleration he experienced and (b) the distance he traveled during this negative acceleration. Figure P2.56 (left) Col. John Stapp and his rocket sled are brought to rest in a very short time interval, (right) Stapps face is contorted by the stress of rapid negative acceleration.A bullet is fired through a board 10.0 cm thick in such a way that the bullets line of motion is perpendicular to the face of the board. If the initial speed of the bullet is 4.00 102 m/s and it emerges from the other side of the board with a speed of 3.00 102 m/s, find (a) the acceleration of the bullet as it passes through the board and (b) the total time the bullet is in contact with the board.A speedboat moving at 30.0 m/s approaches a no-wake buoy marker 1.00 102 m ahead. The pilot slows the boat with a constant acceleration of 3.50 m/s2 by reducing the throttle. (a) How long does it take the boat to reach the buoy? (b) What is the velocity of the boat when it reaches the buoy?A student throws a set of keys vertically upward to his fraternity brother, who is in a window 4.00 m above. The brother's outstretched hand catches the keys 1.50 s later. (a) With what initial velocity were the keys thrown? (b)? What was the velocity of the keys just before they were caught?A student throws a set of keys vertically upward to his fraternity brother, who is in a window a distance h above. The brothers outstretched hand catches the keys on their way up a time t later, (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught? (Answers should be in terms of h, g, and t.)An insect called the froghopper (Philaenus spumarius) has been called the best juniper in the animal kingdom. This insect can accelerate at over 4.0 103 m/s2 during a displacement of 2.0 mm as it straightens its specially equipped jumping legs. (a) Assuming uniform acceleration, what is the insect's speed after it has accelerated through this short distance? (b) How long does it take to reach that speed? (c.) How high could the insect jump if air resistance could be ignored? Note that, the actual height obtained is about 0.70 m, so air resistance is important here.62APA ball is thrown upward from the ground with an initial speed of 25 m/s; at the same instant, another ball is dropped from a building 15 m high. After how long will the balls be at the same height?To pass a physical education class at a university, a student must run 1.0 mi in 12 min. After running for 10 min, she still has 500 yd to go. If her maximum acceleration is 0.15 m/s2, can she make it? If the answer is no, determine what acceleration she would need to be successful.In Chapter 5 we will define the center of mass of an object The center of mass moves with constant acceleration when constant forces act on the object A gymnast jumps straight up, with her center of mass moving at 2.80 m/s as she leaves the ground. How high above this point is her center of mass (a) 0.100 s, (b) 0.200 s, (c) 0.300 s, and (d) 0.500 s thereafter?Two students air on a balcony a distance h above the street. One student throws a ball vertically down-ward at a speed v0; at the same time, the other student throws a ball vertically upward at the same speed. Answer the following symbolically in terms of v0, g, h, and t. (a) Write the kinematic equation for the y-coordinate of each ball, (b) Set the equations found in part (a) equal to height 0 and solve each for t symbolically using the quadratic formula. What is the difference in the two balls' time in the air? (c) Use the time-independent kinematics equation to find the velocity of each ball as it strikes the ground, (d) How far apart are the balls at a time t after they are released and before the strike the ground?You drop a ball from a window on an upper floor of a building and ii is caught by a friend on the ground when the ball is moving with speed vf. You now repeat the drop, but you have a friend on the street below throw another ball upward at speed vf exactly at the same time that you drop your ball from the window. The two balls are initially separated by 28.7 m. (a) At what time do they pass each other? (b) At what location do they pass each other relative the window?The driver of a truck slams on the brakes when he sees a tree blocking the road. The truck slows down uniformly with an acceleration of 5.60 m/s2 for 4.20 s. making skid marks 62.4 m long that end at the tree. With what speed does the truck then strike the tree?Emily challenges her husband, David, to catch a 1 bill as follows. She holds the bill vertically as in Figure P2.67, with the center of the bill between David's index finger and thumb. David must catch the bill after Emily releases it without moving his hand downward. If his reaction time is 0.2 s, will he succeed? Explain your reasoning. (This challenge is a good trick you might want to try with your friends.) Figure P2.67A mountain climber stands at the top of a 50.0-m cliff that overhangs a calm pool of water. She throws two stones vertically downward 1.00 s apart and observes that they cause a single splash. The first stone had an initial velocity of 2.00 m/s. (a) How long after release of the first stone did the two stones hit the water? (b) What initial velocity must the second stone have had, given that they hit the water simultaneously? (c) What was the velocity of each stone at the instant it hit the water?An ice sled powered by a rocket engine sum from rest on a large frozen lake and accelerates at + 40 ft/s2. After some time t1, the rocket engine is shut down and the sled moves with constant velocity v for a time t2. If the total distance traveled by the sled is 17 500 ft and the total time is 90 s. find (a) the times t1 and t2 and (b) the velocity v. At the 17 500-ft mark, the sled begins to accelerate at 20 ft/s2. (c) What is the final position of the sled when it comes to rest? (d) How long does it take to come to rest?In Bosnia, the ultimate test of a young nuns courage used to be to jump off a 400-year-old bridge (destroyed in 1993; rebuilt in 2004) into the River Neretva, 23 m below the bridge. (a) How long did the jump last? (b) How fan was the jumper traveling upon impact with the river? (c) If the speed of sound in air is 340 m/s, how long after the jumper took off did a spectator on the bridge hear the splash?73APA glider on an air track carries a flag of length through a stationary photogate, which measures the time interval td during which the flag blocks a beam of infrared light passing across the photogate. The ratio vd = /td is the average velocity of the glider over this part of its motion. Suppose the glider moves with constant acceleration, (a) Is vd necessarily equal to the instantaneous velocity of the glider when it is halfway through the photogate in space? Explain. (b) Is vd equal to the instantaneous velocity of the glider when it is halfway through the photogate in time? Explain.A stuntman sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 10.0 m/s, and the man is initially 3.00 m above the level of the saddle. (a) What must be the horizontal distance between the saddle and the limb when the man makes his move? (b) How long is he in the air?The magnitudes of two vectors A and B are 12 units and 8 units, respectively. What are the largest and smallest possible values for the magnitude of the resultant vector R = A + B? (a) 14.4 and 4 (b) 12 and 8 (c) 20 and 4 (d) none of these.3.2QQ3.3QQWhich of the following objects cant be accelerating? (a) An object moving with a constant speed; (b) an object moving with a constant velocity; or (c) an object moving along a curve.Consider the following controls in an automobile: gas pedal, brake, steering wheel. The controls in this list that can cause an acceleration of the car are (a) all three controls, (b) the gas pedal and the brake, (c) only the brake, or (d) only the gas pedal.Suppose you are carrying a ball and running at constant velocity on level ground. You wish to throw the ball and catch it as it comes back down. Neglecting air resistance, should you (a) throw the ball at an angle of about 45 above the horizontal and maintain the same speed, (b) throw the ball straight up in the air and slow down to catch it, or (c) throw the ball straight up in the air and maintain the same speed?As a projectile moves in its parabolic path, where are the velocity and acceleration vectors perpendicular to each other? (a) Everywhere along the projectiles path, (b) at the peak of its path, (c) nowhere along its path, or (d) not enough information is given.A vector A has components Ax = 5.00 m and Ay = 9.00 m. Find (a) the magnitude and (b) the direction of the vector. (See Section 3.2.)Calculate (a) the x- and (b) y-components of the vector with magnitude 24.0 m and direction 56.0. (See Section3.2.)Find (a) the x- and (b) y-components of R = 2A B if A has components Ax = 15.0 m and Ay = 12.0 m whereas B has components Bx = 24.0 m and By = 8.00 m. (See Section 3.2.)A hiker walks from (x1, y1) = (4.00 km. 3.00 km) to (x2, y2) = (3.00 km, 6.00 km), (a) What distance has the traveled? (b) The hiker desires to return to his starting point. In what direction should he go? (Give the angle with respect to due cast.) (See Sections 3.2 and 3.3.)A hiker walks 3.00 km north and then 4.00 km west, all in one hour and forty minutes, (a) Calculate his average speed in km/h. (b) Calculate the magnitude of his average velocity. (See Section 3.2 and 3.3.)A car is traveling east at 25.0 m/s when it turns north and accelerates to 35.0 m/s, all during a time of 6.00 s. Calculate the magnitude of the car's average acceleration. (See Section 3.3.)A skier leaves the end of a horizontal ski jump at 22.0 m/s and falls through a vertical distance of 3.20 m before landing. Neglecting air resistance, (a) how long does it take the skier to reach the ground? (b) How far horizontally docs the skier travel in the air before landing? (Sec Section 3.4.)A catapult launches a large stone from ground level at a speed of 45.0 m/s at an angle of 55.0 with the horizontal. The stone returns to ground level shortly thereafter, (a) How long is it in the air? (b) What maximum height does the stone reach? (Neglect, air friction.) (See Section 3.4.)A cruise ship sails due north at 4.50 m/s while a coast guard patrol boat heads45.0 north of west at 5.20 m/s. What are (a) the x- and (b) y-components of the velocity of the cruise ship relative to the patrol boat? (See Section 3.5.)1CQ2CQAs a projectile moves in its path, is there any point along the path where the velocity and acceleration vectors are (a) perpendicular to each other? (b) Parallel to each other?Construct motion diagrams showing the velocity and acceleration of a projectile at several points along its path, assuming (a) the projectile is launched horizontally and (b) the projectile is launched at an angle with the horizontal.Explain whether the following particles do or do not have an acceleration: (a) a particle moving in a straight line with constant speed and (b) a particle moving around a curve with constant speed.A ball is projected horizontally from the top of a building. One second later, another ball is projected horizontally from the same point with the same velocity, (a) At what point in the motion will the balls be closest to each other? (b) Will the first ball always be traveling faster than the second? (c) What will be the time difference between them when the balls hit the ground? (d) Can the horizontal projection velocity of the second ball be changed so that the balls arrive at the ground at the same time?A spacecraft drifts through space at a constant velocity. Suddenly, a gas leak in the side of the spacecraft causes it to constantly accelerate in a direction perpendicular to the initial velocity. The orientation of the spacecraft does not change, so the acceleration remains perpendicular to the original direction of the velocity. What is the shape of the path followed by the spacecraft?Determine which of the following moving objects obey the equations of projectile motion developed in this topic. (a) A ball is thrown in an arbitrary direction. (b) A jet airplane crosses the sky with its engines thrusting the plane forward. (c) A rocket leaves the launch pad. (d) A rocket moves through the sky after its engines have failed. (e) A stone is thrown under water.Two projectiles are thrown with the same initial speed, one at an angle with respect to the level ground and the other at angle 90 . Both projectiles strike the ground at the same distance from the projection point Are both projectiles in the air for the same length of time?A ball is thrown upward in the air by a passenger on a train that is moving with constant velocity, (a) Describe the path of the ball as seen by the passenger. Describe the path as seen by a stationary observer outside the train, (b) How would these observations change if the train were accelerating along the track?A projectile is launched at some angle to the horizontal with some initial speed vi; air resistance is negligible, (a) Is the projectile a freely falling body? (b) What is its acceleration in the vertical direction? (c) What is its acceleration in the horizontal direction?A baseball is thrown from the outfield toward the catcher. When the ball reaches its highest point, which statement is true? (a) Its velocity and its acceleration are both zero, (b) Its velocity is not zero, but its acceleration is zero, (c) Its velocity is perpendicular to its acceleration, (d) Its acceleration depends on the angle at which the ball was thrown, (c) None of statements (a) through (d) is true.A student throws a heavy red ball horizontally from a balcony of a tall building with an initial speed v0. At the same time, a second student drops a lighter blue ball from the same balcony. Neglecting air resistance, which statement is true? (a) The blue ball reaches the ground first, (b) The balls reach the ground at the same instant, (c) The red ball reaches the ground first, (d) Both balls hit the ground with the same speed, (e) None of statements(a) through(d) is true.A car moving around a circular track, with constant speed (a) has zero acceleration, (b) has an acceleration component in the direction of its velocity, (c) has an acceleration directed away from the center of its path, (d) has an acceleration directed toward the center of its path, or (e) has an acceleration with a direction that cannot be determined from the information given.As an apple tree is transported by a truck moving to the right with a constant velocity, one of its apples shakes loose and falls toward the bed of the truck. Of the curves shown in Figure CQ3.13, (i) which best describes the path followed by the apple as seen by a stationary observer on the ground, who observes the truck moving from his left to his right? (ii) Which best describes the path as seen by an observer sitting in the truck? Figure CQ3.131PVector A has a magnitude of 8.00 units and makes an angle of 45.0 with the positive x-axis. Vector B also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods, find (a) the vector sum A + B and (b) the vector difference A B.Vector A is 3.00 units in length and points along the positive x-axis. Vector B is 4.00 units in length and points along the negative y-axis. Use graphical methods to find the magnitude and direction of the vectors (a) A + B and (b) A B.Three displacements are A = 200 m due south, R = 250 m due west, and C = 150 m at 30.0 east of north, (a) Construct a separate diagram for each of the following possible ways of adding these vectors: R1=A+B+C; R2 = B + C + A; R3 = C + B + A. (b) Explain what you can conclude from comparing the diagrams.A roller coaster moves 200 ft horizontally and then rises 135 ft at an angle of 30.0 above the horizontal. Next, it travels 135 ft at an angle of 40.0 below the horizontal. Use graphical techniques to find the roller coaster's displacement from its starting point to the end of this movement.An airplane flies 200 km due west from city A to city B and then 300 km in the direction of 30.0 north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? (b) Relative to city A, in what direction is city C? (c) Why is the answer only approximately correct?A plane flies from base camp to lake A, a distance of 280 km at a direction of 20.0 north of east. After dropping off supplies, the plane flies to lake B, which is 190 km and 30.0 west of north from lake A. Graphically determine the distance and direction from lake B to the base camp.A force F1, of magnitude 6.00 units acts on an object at the origin in a direction = 30.0 above the positive x-axis (Fig. P3.8). A second force F2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F1 + F2?. Figure P3.8A man in a maze makes three consecutive displacements. His first displacement is 8.00 m westward, and the second is 13.0 m northward. At the end of his third displacement he is back to where he started. Use the graphical method to find the magnitude and direction of his third displacement.10PThe magnitude of vector A is 35.0 units and points in the direction 325 counterclockwise from the positive x-axis. Calculate the x- and y-components of this vector.A figure skater glides along a circular path of radius 5.00 m. If she coasts around one half of the circle, find (a) the magnitude of the displacement vector and (b) what distance she skated. (c) What is the magnitude of the displacement if she skates all the way around the circle?A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and then 6.00 blocks east, (a) What is her resultant displacement? (b) What is the total distance she travels?A hiker starts at his camp and moves the following distances while exploring his surroundings: 75.0 m north, 2.50 102 m east, 125 m at an angle 30.0 north of east, and 1.50 102 m south. (a) Find his resultant displacement from camp. (Take east as the positive x-direction and north as the positive y-direction.) (b) Would changes in the order in which the hiker makes the given displacements alter his final position? Explain.A vector has an x-component of 25.0 units and a y-component of 40.0 units. Find the magnitude and direction of the vector.A quarterback takes the ball from the line of scrimmage, runs backwards for 10.0 yards, then runs sideways parallel to the line of scrimmage for 15.0 yards. At this point, he throws a 50.0-yard forward pass straight down field, perpendicular to the line of scrimmage. What is the magnitude of the football's resultant displacement?The eye of a hurricane passes over Grand Bahama Island in a direction 60.0 north of west with a speed of 41.0 km/h. Three hours later the course of the hurricane suddenly shifts due north, and its speed slows to 25.0 km/h. How far from Grand Bahama is the hurricane 4.50 h after it passes over the island?A map suggests that Atlanta is 730 miles in a direction 5.00c north of east from Dallas. The same map shows that Chicago is 560 miles in a direction 21.0 west of north from Atlanta. Figure P3.18 shows the location of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago. Figure P3.18A commuter airplane starts from ar. airport and takes the route shown in Figure P3.19. The plane first flies to city A, located 175 km away in a direction 30.0 north of east. Next, it flies for 150 km 20.0 west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starling point. Figure P3.19The helicopter view in Figure P3.20 shows two people pulling on a stubborn mule. Find (a) the single force that is equivalent to the two forces shown and (b) the force a third person would have to exert on the mule to make the net force equal to zero. The forces are measured in units of newtons (N). Figure P3.20A novice golfer on the green takes three strokes to sink the ball. The successive displacements of the ball are 4.00 m to the north, 2.00 m northeast, and 1.00 m at 30.0 west of south (Fig. P3.21). Starting at the same initial point, an expert golfer could make the hole in what single displacement? Figure P3.21One of the fastest recorded pitches in major league baseball, thrown by Tim Lincecum in 2009, was clocked at 101.0 mi/h (Fig. P3.8). If a pitch were thrown horizontally with this velocity, how far would the ball fall vertically by the time it reached home plate, 60.5 ft away? Figure P3.8 Tim Lincecum throws a baseball.A student stands at the edge of a cliff and throws a stone horizontally over the edge with a speed of 18.0 m/s. The cliff is 50.0 m above a flat, horizontal beach as shown in Figure P3.7. (a) What are the coordinates of the initial position of the stone? (b) What are the components of the initial velocity? (c) Write the equations for the x- and y-components of the velocity of the stone with time, (d) Write the equations for the position of the stone with time, using the coordinates in Figure P3.7. (e) How long after being released does the stone strike the beach below the cliff? (f) With what speed and angle of impact does the stone land? Figure P3.7A rock is thrown upward from the level ground in such a way that the maximum height of its flight is equal to its horizontal range R. (a) At what angle is the rock thrown? (b) In terms of the original range R, what is the range Rmax the rock can attain if it is launched at the same speed but at the optimal angle for maximum range? (c) Would your answer to part (a) be different if the rock is thrown with the same speed on a different planet? Explain.The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45. With what speed must the animal leave the ground to reach that height?The record distance in the sport of throwing cowpats is 81.1 m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45 and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time the projectile was in flight, (c) Qualitatively, how would the answers change if the launch angle were greater than 45? Explain.A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.0 to the horizontal, (a) By how much does the ball clear or fall short of clearing the crossbar? (b) Does the ball approach the crossbar while still rising or while falling?From the window of a building, a ball is tossed from a height y0 above the ground with an initial velocity of 8.00 m/s and angle of 20.0 below the horizontal. It strikes the ground 3.00 s later, (a) If the base of the building is taken to be the origin of the coordinates, with upward the positive y-direction, what are the initial coordinates of the ball? (b) With the positive x-direction chosen to be out the window, find the x- and y-components of the initial velocity, (c) Find the equations for the x- and y-components of the position as functions of time, (d) How far horizontally from the base of the building does the ball strike the ground? (e) Find the height from which the ball was thrown, (f) How long does it take the ball to reach a point 10.0 m below the level of launching?A brick is thrown upward from the top of a building at an angle of 25 to the horizontal and with an initial speed of 15 m/s. If the brick is in flight for 3.0 s, how tall is the building?An artillery shell is fired with an initial velocity of 300 m/s at 55.0 above the horizontal. To clear an avalanche, it explodes on a mountainside 42.0 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to its firing point?A car is parked on a cliff overlooking the ocean on an incline that makes an angle of 24.0 below the horizontal. The negligent driver leaves the car in neutral, and the emergency brakes are defective. The car rolls from rest down the incline with a constant acceleration of 4.00 m/s2 for a distance of 50.0 m to the edge of the cliff, which is 30.0 m above the ocean. Find (a) the cars position relative to the base of the cliff when the car lands in the ocean and (b) the length of time the car is in the air.A fireman d = 50.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of i = 30.0 above the horizontal as shown in Figure P3.18. If the speed of the stream as it leaves the hose is vi = 40.0 m/s, at what height will the stream of water strike the building? Figure P3.18A projectile is launched with an initial speed of 60.0 m/s at an angle of 30.0 above the horizontal. The projectile lands on a hillside 4.00 s later. Neglect air friction, (a) What is the projectiles velocity at the highest point of its trajectory? (b) What is the straight-line distance from where the projectile was launched to where it hits its target?A playground is on the flat roof of a city school, 6.00 m above the street below (Fig. P3.19). The vertical wall of the building is h = 7.00 m high, to form a 1-m-high railing around the play-ground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of = 53.0 above the horizontal at a point d = 24.0 m from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall, (a) Find the speed at which the ball was launched. (b) Find the vertical distance by which the ball clears the wall. (c) Find the horizontal distance from the wall to the point on the roof where the ball lands.A jet airliner moving initially at 3.00 102 mi/h due east enters a region where the wind is blowing 1.00 102 mi/h in a direction 30.0 north of east, (a) Find the components of the velocity of the jet airliner relative to the air, vJA. (b) Find the components of the velocity of the air relative to Earth, vAE. (c) Write an equation analogous to Equation 3.11 for the velocities vJA, vAE, and vJE. (d) What are the speed and direction of the aircraft relative to the ground?A car travels due east with a speed of 50.0 km/h. Raindrops are falling at a constant speed vertically with respect to the Earth. The traces of the rain on the side windows of the car make an angle of 60.0 with the vertical. Find the velocity of the rain with respect to (a) the car and (b) the Earth.A bolt drops from the ceiling of a moving train car that is accelerating northward at a rate of 2.50 m/s2, (a) What is the acceleration of the bolt relative to the train car? (b) What is the acceleration of the bolt relative to the Earth? (c) Describe the trajectory of the bolt as seen by an observer fixed on the Earth.A Coast Guard cutter detects an unidentified ship at a distance of 20.0 km in the direction 15.0 cast of north. The ship is traveling at 26.0 km/h on a course at 40.0 east of north. The Coast Guard wishes to send a speedboat to intercept and investigate the vessel, (a) If the speedboat travels at 50.0 km/h, in what direction should it head? Express the direction as a compass bearing with respect to due north, (b) Find the time required for the cutter to intercept the ship.An airplane maintains a speed of 630 km/h relative to the air it is flying through, as it makes a trip to a city 750 km away to the north, (a) What time interval is required for the trip if the plane flies through a headwind blowing at 35.0 km/h toward the south? (b) What time interval is required if there is a tailwind with the same speed? (c) What time interval is required if there is a crosswind blowing at 35.0 km/h to the east relative to the ground?Suppose a chinook salmon needs to jump a waterfall that is 1.50 m high. If the fish starts from a distance 1.00 m from the base of the ledge over which the waterfall flows, (a) find the x- and y-components of the initial velocity the salmon would need to just reach the ledge at the top of its trajectory, (b) Can the fish make this jump? (Note that a Chinook salmon can jump out of the water with an initial speed of 6.26 m/s.)A river has a steady speed of 0.500 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point, (a) If the student can swim at a speed of 1.20 m/s in still water, how long does the trip take? (b) How much time is required in still water for the same length swim? (c) Intuitively, why does the swim take longer when there is a current?This is a symbolic version of Problem 29. A river has a steady speed of vs. A student swims upstream a distance d and back to the starting point. (a) If the student can swim at a speed of v in still water, how much time tup does it take the student to swim upstream a distance d? Express the answer in terms of d, v, and vs. (b) Using the same variables, how much time tdown does it take to swim back downstream to the starting point? (c) Sum the answers found in parts (a) and (b) and show that the time ta required for the whole trip can be written as ta=2d/v1-vs2/v2 (d) How much time tb does the trip take in still water? (e) Which is larger, ta or tb? Is it always larger?An airplane maintains a speed of 630 km/h relative to the air it is flying through, as it makes a trip to a city 750 km away to the north. (a) What time interval is required for the trip if the plane flies through a headwind blowing at 35.0 km/h toward the south? (b) What time interval is required if there is a tailwind with the same speed? (c) What time interval is required if there is a crosswind blowing at 35.0 km/h to the east relative to the ground?A moving walkway at an airport has a speed v1 and a length L. A woman stands on the walkway as it moves from one end to the other, while a man in a hurry to reach his flight walks on the walkway with a speed of v2 relative to the moving walkway, (a) How long does it take the woman to travel the distance L? (b) How long does it take the man to travel this distance?How long does it take ail automobile traveling in the left lane of a highway at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 40.0 km/h when the cars front bumpers are initially 100 m apart?You can use any coordinate system you like to solve a projectile motion problem. To demonstrate the truth of this statement, consider a ball thrown off the top of a building with a velocity v at an angle with respect to the horizontal. Let the building be 50.0 m tall, the initial horizontal velocity be 9.00 m/s, and the initial vertical velocity be 12.0 m/s. Choose your coordinates such that the positive y-axis is upward, the x-axis is to the right, and the origin is at the point where the ball is released, (a) With these choices, find the balls maximum height above the ground and the time it takes to reach the maximum height. (b) Repeat your calculations choosing the origin at the base of the building.A Nordic jumper goes off a ski jump at an angle of 10.0 below the horizontal, traveling 108 m horizontally and 55.0 m vertically before landing. (a) Ignoring friction and aerodynamic effects. calculate the speed needed by the skier on leaving the ramp. (b) Olympic Nordic jumpers can make such jumps with a jump speed of 23.0 m/s, which is considerably less than the answer found in pan (a). Explain how that is possibleIn a local diner, a customer slides an empty coffee cup down the counter for a refill. The cup slides off the counter and strikes the floor at distance d from the base of the counter. If the height of the counter is h, (a) find an expression for the time t it takes the cup to fall to the floor in terms of the variables h and g. (b) With what speed does the mug leave the counter? Answer in terms of the variables d, g, and h. (c) In the same terms, what is the speed of the cup immediately before it hits the floor? (d) In terms of h and d, what is the direction of the cups velocity immediately before it hits the floor?Towns A and B in Figure P3.35 are 80.0 km apart. A couple arranges to drive from town A and meet a couple driving from town B at the lake, L. The two couples leave simultaneously and drive for 2.50 h in the directions shown. Car 1 has a speed of 90.0 km/h. If the cars arrive simultaneously at the lake, what is the speed of car 2? Figure P3.35A chinook salmon has a maximum underwater speed of 3.58 m/s, but it can jump out of water with a speed of 6.26 m/s. To move upstream past a waterfall, the salmon does not need to jump to the top of the fall, but only to a point in the fall where the water speed is less than 3.58 m/s; it can then swim up the fall for the remaining distance. Because the salmon must make forward progress in the water, lets assume it can swim to the top if the water speed is 3.00 m/s. If water has a speed of 1.50 m/s as it passes over a ledge, (a) how far below the ledge will the water be moving with a speed of 3.00 m/s? (Note that water undergoes projectile motion once it leaves the ledge.) (b) If the salmon is able to jump vertically upward from the base of the fall, what is the maximum height of waterfall that the salmon can clear?A rocket is launched at an angle of 53.0 above the horizontal with an initial speed of 100. m/s. The rocket moves for 3.00 s along its initial line of motion with an acceleration of 30.0 m/s2. At this time, its engines fail and the rocket proceeds to move as a projectile. Find (a) the maximum altitude reached by the rocket, (b) its total time of flight, and (c) its horizontal range.Two canoeists in identical canoes exert the same effort paddling and hence maintain the same speed relative to the water. One paddles directly upstream (and moves upstream), whereas the other paddles directly downstream. With downstream as the positive direction, an observer on shore determines the velocities of the two canoes to be 1.2 m/s and + 2.9 m/s, respectively, (a) What is the speed of the water relative to the shore? (b) What is the speed of each canoe relative to the water?(a) If a person can jump a maximum horizontal distance (by using a 45 projection angle) of 3.0 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g = 9.80 m/s2? (b) Repeat for Mars, where the acceleration due to gravity is 0.38g.A farm truck travels due east with a constant speed of 9.50 m/s along a horizontal road. A boy riding in the back of the truck tosses a can of soda upward (Fig. P3.40) and catches it at the same location in the truck bed, but 16.0 m farther down the road. Ignore any effects of air resistance. (a) At what angle to the vertical does the boy throw the can, relative to the moving truck? (b) What is the cans initial speed relative to the truck? (c) What is the shape of the cans trajectory as seen by the boy? (d) What is the shape of the cans trajectory as seen by a stationary observer on the ground? (e) What is the initial velocity of the can, relative to the stationary observer? Figure P3.40A home run is hit in such a way that the baseball just clears a wall 21 m high, located 130 m from home plate. The ball is hit at an angle of 35 to the horizontal, and air resistance is negligible. Find (a) the initial speed of the ball, (b) the time it takes the ball to reach the wall, and (c) the velocity components and the speed of the ball when it reaches the wall. (Assume the ball is hit at a height of 1.0 m above the ground.)A ball is thrown straight upward and returns to the throwers hand after 3.00 s in the air. A second ball thrown at an angle of 30.0 with the horizontal reaches the same maximum height as the first ball, (a) At what speed was the first ball thrown? (b) At what speed was the second ball thrown?A quarterback throws a football toward a receiver with an initial speed of 20. m/s at an angle of 30. above the horizontal. At that instant the receiver is 20. m from the quarterback. In (a) what direction and (b) with what constant speed should the receiver run in order to catch the football at the level at which it was thrown?A 2.00-m-tall basketball player is standing on the floor 10.0 m from the basket, as in Figure P3.44. If he shoots the ball at a 40.0 angle with the horizontal, at what initial speed must he throw the basketball so that it goes through the hoop without striking the backboard? The height of the basket is 3.05 m. Figure P3.44In a very popular lecture demonstration, a projectile is fired at a falling target as in Figure P3.59. The projectile leaves the gun at the same instant the target is dropped from rest. Assuming the gun is initially aimed at the target, show that the projectile will hit the target. (One restriction of this experiment is that the projectile must reach the target before the target strikes the floor. Figure P3.59Figure P3.60 illustrates the difference in proportions between the male (m) and female (f) anatomies. The displacements d1m. and d1f from the bottom of the feet to the navel have magnitudes of 104 cm and 84.0 cm, respectively. The displacements d2m and d2f have magnitudes of 50.0 cm and 43.0 cm, respectively. (a) Find the vector sum of the displacements dd1 and dd2 in each case. (b) The male figure is 180 cm tall, the female 168 cm. Normalize the displacements of each figure to a common height of 200 cm and re-form the vector sums as in part (a). Then find the vector difference between the two sums. Figure P3.60By throwing a ball at an angle of 45, a girl can throw the ball a maximum horizontal distance R on a level field. How far can she throw the tame ball vertically upward? Assume her muscles give the ball the same speed in each case. (Is this assumption valid?)The equation of a parabola is y = ax2 + bx + c, where a, b, and c are constants. The x- and y-coordinates of a projectile launched from the origin as a function of time are given by x = v0xt and y=v0yt12gt2, where v0x. and v0y, are the components of the initial velocity. (a) Eliminate t from these two equations and show that the path of a projectile is a parabola and has the form y = ax + bx2. (b) What are the values of a, b, and c for the projectile?A hunter wishes to cross a river that is 1.5 km wide and flows with a speed of 5.0 km/h parallel to its banks. The hunter uses a small powerboat that moves at a maximum speed of 12 km/h with respect to the water. What is the minimum time necessary for crossing?When baseball outfielders throw the ball, they usually allow it to take one bounce, on the theory that the ball arrives at its target sooner that way. Suppose that, after the bounce, the ball rebounds at the same angle that it had when it was released (as in Fig. P3.48), but loses half its speed, (a) Assuming that the ball is always thrown with the same initial speed, at what angle should the ball be thrown in order to go the same distance D with one bounce as a ball thrown upward at 45.0 with no bounce? (b) Determine the ratio of the times for the one-bounce and no-bounce throws. Figure P3.48A daredevil is shot out of a cannon at 45.0 to the horizontal with an initial speed of 25.0 m/s. A net is positioned a horizontal distance of 50.0 m from the cannon. At what height above the cannon should the net be placed in order to catch the daredevil?Chinook salmon are able to move upstream faster by jumping out of the water periodically; this behavior is called porpoising. Suppose a salmon swimming in still water jumps out of the water with a speed of 6.26 m/s at an angle of 45, sails through the air a distance L before returning to the water, and then swims a distance L underwater at a speed of 3.58 m/s before beginning another porpoising maneuver. Determine the average speed of the fish.A student derides to measure the muzzle velocity of a pellet shot from his gun. He points the gun horizontally. He place a target on a vertical wall a distance x away from the gun. He pellet hits the target a vertical distance y below the gun. (a) Show that the position of the pellet when traveling through the air is given by y = Ax2, where A it a constant. (b) Express the constant A In terms of the initial (muzzle) velocity and the free-fall acceleration. (c) If x = 3.00 m and y = 0 210 m, what is the initial speed of the pellet?A golf ball with an initial speed of 50.0 m/s lands exactly 240 m downrange on a level course, (a) Neglecting air friction, what two projection angles would achieve this result? (b) What is the maximum height reached by the ball, using the two angles determined in part (a)?A landscape architect is planning an artificial waterfall in a city park. Water flowing at 0.750 m/s leaves the end of a horizontal channel at the top of a vertical wall h = 2.35 m high and falls into a pool (Fig. P3.54). (a) How far from the wall will the water land? Will the space behind the waterfall be wide enough for a pedestrian walkway? (b) To sell her plan to the city council, the architect wants to build a model to standard scale, one-twelfth actual size. How fast should the water flow in the channel in the model? Figure P3.54One strategy in a snowball fight is to throw a snowball at a high angle over level ground. Then, while your opponent is watching that snowball, you throw a second one at a low angle timed to arrive before or at the same time as the first one. Assume both snowballs are thrown with a speed of 25.0 m/s. The first is thrown at an angle of 70.0 with respect to the horizontal. (a) At what angle should the second snowball be thrown to arrive at the same point as the first? (b) How many seconds later should the second snowball be thrown after the first for both to arrive at the same time?A dart gun is fired while being held horizontally at a height of 1.00 m above ground level and while it is at rest relative to the ground. The dart from the gun travels a horizontal distance of 5.00 m. A college student holds the same gun in a horizontal position while sliding down a 45.0 incline at a constant speed of 2.00 m/s. How far w ill the dart travel if the student fires the gun when it is 1.00 m above the ground?The determined Wile E. Coyote is out once more to try to capture the elusive roadrunner. The coyote wears a new pair of power roller skates, which provide a constant horizontal acceleration of 15.0 m/s2, as shown in Figure P3.59. The coyote starts off at rest 70.0 m from the edge of a cliff at the instant the roadrunner zips in the direction of the cliff, (a) If the roadrunner moves with constant speed, find the minimum speed the roadrunner must have to reach the cliff before the coyote. (b) If the cliff is 1.00 102 m above the base of a canyon, find where the coyote lands in the canyon. (Assume his skates are still in operation when he is in flight and that his horizontal component of acceleration remains constant at 15.0 m/s2.) Figure P3.59A truck loaded with cannonball watermelons stops suddenly to avoid running over the edge of a washed-out bridge (Fig. P3.74). The quick stop causes a number of melons to fly off the truck. One melon rolls over the edge with an initial speed i = 10.0 m/s in the horizontal direction. A cross section of the bank has the shape of the bottom half of a parabola with its vertex at the edge of the road, and with the equation y2 = (16.0 m) x, where x and y are measured in meters. What are the x- and y-coordinates of the melon when it splatters on the bank? Figure P3.74 The blue dashed curve shows the parabolic shape of the bank.Which of the following statements are true? (a) An object can move even when no force acts on it. (b) If an object isnt moving, no external forces act on it. (c) If a single force acts on an object, the object accelerates. (d) If an object accelerates, at least one force is acting on it. (e) If an object isnt accelerating, no external force is acting on it. (f) If the net force acting on an object is in the positive x-direction, the object moves only in the positive x-direction.Which has greater value, a newton of gold on Earth or a newton of gold on the Moon? (a) The newton of gold on the Earth. (b) The newton of gold on the Moon. (c) The value is the same, regardless.Respond to each statement, true or false: (a) No force of gravity acts on an astronaut in an orbiting space station. (b) At three Earth radii from the center of Earth, the acceleration of gravity is one-ninth its surface value. (c) If two identical planets, each with surface gravity g and volume V, coalesce into one planet with volume 2V, the surface gravity of the new planet is 2g. (d) One kilogram of gold would have greater value on Earth than on the Moon.A small sports car collides head-on with a massive truck. The greater impact force (in magnitude) acts on (a) the car, (b) the truck, (c) neither, the force is the same on both. Which vehicle undergoes the greater magnitude acceleration? (d) the car, (e) the truck, (f) the accelerations are the same.Consider the two situations shown in Figure 4.30, in which there is no acceleration. In both cases the men pull with a force of magnitude F. Is the reading on the scale in part (i) of the figure (a) greater than, (b) less than, or (c) equal to the reading in part (ii)?For the woman being pulled forward on the toboggan in Figure 4.33, is the magnitude of the normal force exerted by the ground on the toboggan (a) equal to the total weight of the woman plus the toboggan, (b) greater than the total weight, (c) less than the total weight, or (d) possibly greater than or less than the total weight, depending on the size of the weight relative to the tension in the rope?If you press a book flat against a vertical wall with your hand, in what direction is the friction force exerted by the wall on the book? (a) downward (b) upward (c) out from the wall (d) into the wall.A crate is sitting in the center of a flatbed truck. As the truck accelerates to the east, the crate moves with it, and doesnt slide on the bed of the truck. In what direction is the friction force exerted by the bed of the truck on the crate? (a) To the west, (b) To the east, (c) There is no friction force because the crate isnt sliding.