(Conceptual Questions): 1. What equation would you use to describe the horizontal acceleration of a ball being thrown? 2. Give an example of an object that would have horizontal acceleration? 3. The horizontal motion and vertical motion of a ball being thrown are dependent or independent of one another? 4. (True or False) The horizontal velocity v x is constant (v x = v ox )? 5. What is the acceleration of the vertical motion of a ball being thrown in the air? (Problems) 1. Mark rolls a boulder off a cliff located 22 meters above the beach. If he s able to impart a velocity of 0.65 meters per second to the boulder, how many meters from the base of the cliff will the boulder land? 2. A car flies off a flat embankment with a velocity of 132 kilometers per hour parallel to the ground 45 meters below. With what velocity does the car ultimately crash into the ground? 3. Alicia kicks a soccer ball with a velocity of 10 meters per second at a 60 degree angle relative to the ground. What is the horizontal component of the velocity? 4. The punter for the Jacksonville Jaguars kicks a football with a n initial velocity of 18 meters per second at a 75-degree angle to the horizontal. What is the vertical component of the ball s velocity at the zenith of its path? 5. A cannonball fired at a 20-degree angle to the horizontal travels with a speed of 25 meters per second. How many meters away does the cannonball land if it falls to the ground at the same height from which it launched. 6. The current world-record motorcycle jump is 77.0 m, set by Jason Renie. Assume that he left the take-off ramp at 12.0 degrees to the horizontal and that the take-off and landing heights are the same. Neglecting air drag, determine his take off speed.
7. A stone is thrown horizontally at a speed of 5.0 m/s from the top of a cliff that is 78.4 m high. a. How long does it take the stone to reach the bottom of the cliff? b. How far from the base of the cliff does the stone hit the ground? c. What are the horizontal and vertical components of the stone s velocity just before it hits the ground? 8. Lucy and her friend are working at an assembly plant making wooden toy giraffes. At the end of the line, the giraffes go horizontally off the edge of the conveyer belt and fall into a box below. If the box is 0.6 m below the level of the conveyor belt and 0.4 m away from it, what must be the horizontal velocity of giraffes as they leave the conveyor belt? 9. A ball is launched at 4.5 m/s at 66 above the horizontal. What are the maximum height and flight time of the ball? 10. Courtney kicks a soccer ball at rest on level ground giving it an initial velocity of 7.8 m/s at an angle of 32. (a) How long will the ball be in the air? (b) How high will the ball go? (c) What will be its range? 11. A player kicks a football from ground ground level with an initial velocity of 27.0 m/s, 30 above the horizontal. Find each of the following. Assume that air resistance is negligible. (a) The ball s hang time? (b) The ball s maximum height? (c) The ball s range? 12. The player in problem 11 then kicks the ball with the same speed, but at angle of 60 from the horizontal. (a) The ball s hang time? (b) The ball s maximum height? (c) The ball s range?
13. A rock is thrown from a 50.0 m high cliff with an initial velocity of 7.0 m/s at an angle of 53.0 above the horizontal. Find the velocity vector for when it hits the ground below. 14. A softball is tossed into the air at an angle of 50.0 with the vertical at an initial velocity of 11.0 m/s. What is its maximum height? 15. A tennis ball is thrown out a window 28 m above the ground at an initial velocity of 15.0 m/s and 20.0 below the horizontal. How far does the ball move horizontally before it hits the ground? 16. You took a running leap off a high-diving platform. You were running at 2.8 m/s and hit the water 2.6 s later. How high was the platform, and how far from the edge of the platform did you hit the water? Ignore air resistance. (How far from the edge of the platform is asking the horizontal distance). 17. A dart player throws a dart horizontally at 12.4 m/s. The dart hits the board 0.32 m below the height from which it was thrown. How far away is the player from the board? 18. An arrow is shot at 30.0 above the horizontal. Its velocity is 49 m/s, and it hits the target. (a) What is the maximum height the arrow will attain? (b) The target is at the height from which the arrow was shot. How far away is it? 19. Divers in Acapulco dive from a cliff that is 61 m high. If the rocks below the cliff extend outward for 23 m, what is the minimum horizontal velocity a diver must have to clear the rocks? 20. A basketball player is trying to make a half-court jump shot and releases the ball at the height of the basket. Assuming that the ball is launched at 51.0, 14.0 m from the basket, what speed must the player give the ball?
21. The figure below shows a pirate ship 560 m from a fort defending a harbor entrance. A defense cannon, located at sea level, fires balls at initial speed v o = 82 m/s. (a) At what initial angle θ o from the horizontal must a ball be fired to hit the ship? (b) What is the maximum range of the cannonballs? 22. At time t = 0, a golf ball is shot from ground level into the air, as indicated in the picture). The angle θ between the ball s direction of travel and the positive direction of the x axis is given in figure (b) as a function of time t. The ball lands at t= 6.00 s. What is the magnitude v o of the ball s launch velocity, at what height y above the launch level does the ball land, and what is the ball s direction of travel just as it lands? 23. A certain airplane has a speed of 290.0 km/h and is diving at an angle of θ = 30.0 below the horizontal when the pilot releases a radar decoy. The horizontal distance between the release point and point where the decoy strikes the ground is d = 700 m. (a) How long is the decoy in the air? (b) How high was the release point?
24. You throw a ball toward a wall at a speed of 25.0 m/s and at an angle of θ o = 40.0 above the horizontal. The wall is a distance of d = 22.0 m from the release point of the ball. (a) How far above the release point does the ball hit the wall? (b) What is the horizontal component of the ball s velocity as it hits the wall? (c) What is the vertical component of the ball s velocity as it hits the wall? (d) When it hits, has it passed the highest point on its trajectory?
ANSWERS: 1. 1.4 m (first find the time by using the vertical equations, then use x=vt to find the distance from the cliff). 2. 47.2 m/s 3. v x = vcosθ = 5.0 m/s 4. 0 m/s 5. 41 m. 6. 43.1 m/s (155 km/h) 7. a. 4.00 s b. 20 m c. v x = 5.0 m s ; v y = 39.2 m s 8. 1 m/s 9. (a) y max = 0.86 m (b) t = 0.84 s 10. (a) t = 1.2s (b) y max = 1.7 m (c) R = 9.84 m 11. (a) t = 2.76 s (b) y max = 9.30 m (c) R = 64.5 m 12. (a) t = 4.77 s (b) y max = 64.4 m
(c) R = 27.9 m 13. 32 m/s at 83 from the horizontal. 14. 2.55 m 15. 27.1 m 16. y = 33 m ; x = 7.3 m 17. 3.2 m 18. (a) 31 m (b) 210 m 19. 6.5 m/ 20. 11.8 m/s at 51 21. (a) θ o = 27 and θ o = 63 (b) R = 686 m. (Note: The max angle is 45 degrees) 22. v o = 39.8 m s ; y = 59 m ; θ = 71 23. (a) 10.0s (b) 897 m 24. (a) 12m (b) 19.2 m/s (c) 4.80 m/s (d) Since v y > 0 when the ball hits the wall, it has not reached the highest point yet.