PC141-PC161 final exam solutions (2) (2)

1. You launch a projectile in the air from a height of 50 ft. The velocity of the ball, v(t) is represented in the following table. Give the best estimate for: a. how fast the ball is traveling at 6 seconds. b. the height of the ball at 6 seconds. 0. 4. 6. 8. 10 v(t) 750 686 622 558 494 430

Mount Olympus is the largest known mountain in the Solar System. It is located in the western hemisphere of the planet Mars. An astronaut launches a measuring instrument from the top of this mountain upwards with an initial velocity of 25 m / s. Upon his return, the astronaut cannot catch the instrument so it begins to descend towards the Martian surface. Determine a. The time required for the instrument to reach its maximum heightb. Maximum heightc. The time required for the instrument to return to the height from which it was launched and its speed at that instant.d. The time required for the stone to reach the surface of Mars.e. Repeat all the previous items assuming Mount Olympus was on Earth.

Question A1 An object slides off a frictionless, horizontal table from a height of 1.40 m above the floor. It strikes the floor a distance of 1.88 m from the base of the table. a) Calculate the speed with which the object leaves the table. b) Calculate the velocity (magnitude and direction) of the object just before it strikes the floor.

An object thrown vertically upward from the surface of a celestial body at a velocity of24  ​m/s reaches a height of s=−0.3t^2+24t meters in t seconds.   a. Determine the velocity v of the object after t seconds. b. When does the object reach its highest​ point? c. What is the height of the object at the highest​ point? d. When does the object strike the​ ground? e. With what velocity does the object strike the​ ground? f. On what intervals is the speed​ increasing?

1. You are on a different planet, and you have been tasked to determine the acceleration of gravity on this rather small planet. You climb a top a cliff that is 100.0 m high. You have two balls, and decided to drop one of them from the edge of this cliff. The ball’s final velocity as it hits the ground is 20.0 m/s. Calculate the acceleration due to gravity on this planet and the time it takes for that ball to reach the ground.a. You then roll the other ball at 10.0 m/s horizontally off the cliff. How far does this ball travel horizontally before it hits the ground?2. Now you are back on Earth. You climb up a top a 100.0 m high cliff and drop a similar ball from the edge of this cliff. How much time will it take for that ball to reach the ground?  please show work so I can understand too please!

1. A scientist suggested that sending people to Mars using a 250-m long cannon would fire people in a space capsule using a speed of 11.10 km/s. What is the acceleration? Comparing to gravitational acceleration, what can you imply with the data? 2. A particle in a constant acceleration has a velocity of 11.20 cm/s in the positive x direction when its x-coordinate is 4.00 cm. If its x-coordinate 3.00s later is -8.00 cm, what is its acceleration (in m/s2)? 3. A boat with a velocity of 27 m/s approaches a marker 98 m ahead. Because of this, the pilot decelerates the boat with a constant acceleration of -2.80 m/s2. (a) How long does it take the boat to reach the marker? Choose the smaller value for time for a quadratic equation. (b) What is the velocity of the boat when it reaches the marker?

Draw each of the following vectors, then find its x- and y-components.a. d→ = (100 m, 45° below +x-axis)b. ν→ = (300 m/s, 20° above +x-axis)c. a→ = (5.0 m/s2, -y-direction)

A ball starts from rest and accelerates at 0.5 m/s² while moving down on a 9 m long inclined plane. 10) When the ball reaches the bottom of this plane, it continues moving with constant velocity along 12 m long horizontal path. Then, it moves up the second inclined surface for 10s and it stops. a) What is the speed of the ball at the bottom of the first inclined plane? b) How long does it take for the ball to reach the bottom of the second inclined plane? c) What is the acceleration in the second inclined plane? d) What is the speed of the ball at the point 8 m away from the bottom of the second inclined plane? Answers: a) v = 3 m/s, b) t = 10 s, c) a = -0.3 m/s² (parallel to that surface and in the downward direction), d) v =2.05 m/s

Q4. A man throws a ball vertically upward from the window of a building with a speed of 15 m/s. The window is 2.0 m above the ground. How long is the ball in air before it hits the ground? A) 3.2s B) 2.7 s C) 2.5 s D) 1.7 s E) 4.4 s

3.) You throw a ball straight up. The ball leaves your hand at a height of 2.00 m above the ground with a speed of 20.0 m/s (~45 mph). Ignore air resistance and use g = 10.0 m/s2 to answer the following questions. You can use a spreadsheet but show your sample calculations. 3a.) Calculate the height, y(t), and velocity, vy(t), at 0.50 second intervals until the ball hits the ground. Show your results in a table and put the units in the column headers: t (s), vy (m/s), y (m). 3b.) Use this data to draw a motion diagram for the ball at 0.50 second intervals. Label the height and the speed at each time interval. Label the origin, starting height, maximum height, and final height. Include the velocity vectors for each time and location of the ball. 3c.) Calculate the time it takes for the ball to hit the ground and the final velocity of the ball just as it hits the ground. Include this velocity vector in your diagram.

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Draw each of the following vectors, then find its x- and y-components.a. d→ = (2.0 km, 30° left of +y-axis)b. ν→ = (5.0 cm/s, -x-direction)c. a→ = (10 m/s2, 40° left of -y-axis)

Suppose a stone is thrown vertically upward from the edge of acliff on Earth with an initial velocity of 64 ft/s from a height of32 ft above the ground. The height (in feet) of the stone above theground t seconds after it is thrown is s(t) = -16t2 + 64t + 32.a. Determine the velocity v of the stone after t seconds.b. When does the stone reach its highest point?c. What is the height of the stone at the highest point?d. When does the stone strike the ground?e. With what velocity does the stone strike the ground?f. On what intervals is the speed increasing?

3. You throw a ball straight from a roof top 160 ft high with an initial speed of 48 ft/s. The formula h = -16t2 + 48t + 160 describes the ball"s height above the ground, h in ft, t in seconds after you throw it. a)When will the ball be 192 ft high? b)When will the ball hit the ground? un in the

A ball is thrown from the ground to a maximum height of 12.4 meters, landing on a roof 4.2m high, 16 meters away. 12.4m 16m 4.2m a. Calculate the initial vertical velocity. b. Calculate the time it takes for the ball to reach maximum height, then the time it takes for it to fall back down, to get the total time in the air. c. Calculate the horizontal velocity. d. Calculate the total initial velocity (both magnitude and direction).

2. In Figure 2, someone is throwing a rock off of a cliff. Suppose that this person wants the rock to hit the plain without hitting the dam or lake. To accomplish this, what is the minimum speed with which she must throw the rock? How far from the dam does the rock land? 1 20.0 ms Cliff 100.0 m Lake Dam 25.0 m Plain Figure 2: This is the figure for question 2.