A projectile is fixed at a certain angle on a plane surface to reach a maximum range with a velocity of 10 m/s.What is the time to reach the ground surface?b. What is the maximum height reached by the projectile?What is the distance travelled by the projectile?а.С.d. Calculate that "certain angle" using differential calculus. (Use the principle of Maxima-Minima)

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Answered: A projectile is fixed at a certain…

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter3: Vectors And Two-Dimensional Motion

Section: Chapter Questions

Problem 69AP: A golf ball with an initial speed of 50.0 m/s lands exactly 240 m downrange on a level course, (a)...

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Unreasonable Results (a) Find the maximum range of a super cannon that has a muzzle velocity of 4.0 km/s. (b) What is unreasonable about the range you found? (c) Is the premise unreasonable or is the available equation inapplicable? Explain your answer. (d) If such a muzzle velocity could be obtained, discuss the effects of air resistance, thinning air with altitude, and the curvature of the Earth on the range of the super cannon.
A river is moving east at 4 m/s. A boat starts from the dock heading 30 north of west at 7 m/s. If the river is 1800 m wide, (a) what is the velocity of the boat with respect to Earth and (b) how long does it take the boat to cross the river?
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 P3.7
(a) A daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a 32° ramp at a speed of 40.0 m/s (144 km/h). How many buses can he clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are 20.0 m long? (b) Discuss what your answer implies about the margin of error in this act—that is, consider how much greater the range is than the horizontal distance he must travel to miss the end of the last bus. (Neglect air resistance.)
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?
Peter throws a baseball through a houses window. He stands 3.4 m from the window. The ball starts in his hand 1.1m above the ground and goes through the window at a point 2.4 m off the ground. a. Sketch the problem, including an xy coordinate system with the origin on the ground directly below the initial position of the ball, the y axis pointing upward, and the x axis pointing toward the house. b. What are the initial and final coordinates of the ball?
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 P3.7
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)?
Unreasonable Results Suppose you wish to shoot supplies straight up to astronauts in an orbit 36,000 km above the surface of the Earth. (a) At what velocity must the supplies be launched? (b) What is unreasonable about this velocity? (c) Is there a problem with the relative velocity between the supplies and the astronauts when the supplies reach their maximum height? (d) Is the premise unreasonable or is the available equation inapplicable? Explain your answer.
Problems 74 and 75 are paired. 74. N A classroom clock has a small magnifying glass embedded near the end of the minute hand. The magnifying glass may be modeled as a particle. Class begins at 7:55 and ends at 8:50. The length of the minute hand is 0.300 m. a. Find the average velocity of the magnifying glass at the end of the minute hand using the coordinate system shown in Figure P3.74. Give your answer in component form. b. Find the magnitude and direction of the average velocity. c. Find the average speed and in the CHECK and THINK step, compare to the average velocity.
A newspaper boy throws papers sideways onto the porches of his customers while riding his bicycle along the sidewalk. The sidewalk is 15 m in front of the porches. The boy throws the papers at the horizontal speed of 6.0 m/s relative to himself, and rides the bieycie at a speed of 4.0 m/s relative to the sidewalk. (a) With what horizontal speed do the papers actually travel relative to the ground? (b) How far in advance of a porch should the boy throw a paper, so that it lands on target? (c) If he waits until he is directly opposite a porch, at what horizontal angle with respect to the sidewalk will he have to throw the paper, to hit the porch?
A projectile starting from ground hits a target on the ground located at a distance of 1000 meters after 40 seconds.a) What is the size of the angle θ?b) At what initial velocity was the projectile launched?

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