Physics 1 - preAP 2 – Dimensional and Relative Motion Problem Set
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Part I: Horizontal Launch
1. A stone is thrown horizontally at 8.0 m/s from a cliff 78.4 high. How far from the base of the cliff does the stone strike the ground?
2. A toy car rolls off the edge of a platform with a velocity of 2.5 m/s. The car hits the ground 4.5 m from the end of the platform. How high above the ground is the platform? What is the velocity at impact? (16 m)
3. A toy car runs off the edge of a table that is 1.225 m. high. If the car lands 0.400 m from the base of the table,
a) How long does it take for the car to fall?
b) What is the horizontal velocity of the car?
4. Victoria jumps off a high-diving platform with a horizontal velocity of 2.8 m/s and lands in the water 2.6 sec later. How high is the platform, and how far from the base of the platform does she land?
5. An airplane traveling 1001 m above the ocean at 125 km/hr is to drop a box of supplies to shipwrecked victims below. At what distance (in front of the victims) should the box be dropped? How many seconds before being directly overhead?
6. A dart player throws a dart horizontally at a speed of 12 m/s. The dart hits the board 0.3 m below the height from
which it was thrown. How far away is the player from the board? (2.9 m)
7. Divers at Acapulco dive from a cliff that is 60 m high. If the rocks below the cliff extend outward for 20 m, what is
the minimum horizontal velocity a diver must have to clear the rocks safely and what is their velocity as they enter the water? (5.7 m/s)
8. Two youngsters dive off an overhang into a lake. Diver 1 drops straight down, diver 2 runs off the cliff with an initial horizontal speed vo. Is the splashdown speed of diver 2 (a) greater than, (b) less than, or (c) equal to the splashdown speed of diver 1?
9. A mountain climber encounters a crevasse in an ice field. The opposite side of the crevasse is 2.75 m lower, and is separated horizontally by a distance of 4.10 m. To cross the crevasse, the climber gets a running start and jumps in the horizontal direction. What is the minimum speed needed to safely cross the distance? (5.48 m/s)
10. A person standing at the edge of a seaside cliff kicks a stone over the edge with a horizontal speed of 18 m/s. If the cliff is 52 m above the water, with what velocity does it strike the water?
Part II: Launched at any angle
11. A projectile has an initial velocity of 20 m/s at an angle of 53o above the horizontal. Find:
a) The vertical (vy) and horizontal (vx) velocities
b) The maximum height of its trajectory. (13 m)
c) How long is it in the air? (3.3 s)
d) The range of its trajectory. (39 m)
e) The horizontal distance from the starting point after 2.0 s. (24 m)
f) The vertical distance from the starting point after 2.0 s. (12 m)
12. A batter hitting a fly ball gives it an initial velocity of 30 m/s at an angle of 30o with the level ground.
How far from the batter will the ball land on the ground? (78 m)
13. An arrow is shot at a 30.0o angle from the horizontal. It has a velocity of 49 m/s.
a) How high will the arrow go?
b) What horizontal distance does it travel?
14. A famous motorcyclist plans to jump across a canyon 3.5 km wide. To do this, he plans to leave a
30o ramp on one side of the canyon at a speed of 196 m/s. If he attains this speed, will he
reach the other side of the canyon on the jump or do we send a get-well card?
15. A projectile is fired such that the vertical component of its velocity is 49 m/s. The horizontal component of its velocity is 60 m/s. How long is it in the air and what is its range?
16. While standing on an open bed of a truck moving at 35 m/s (really dumb!), an archer sees a duck flying directly overhead. The archer shoots an arrow at the duck and misses. The arrow leaves the bow with a vertical velocity of 98 m/s. How long does it remain in the air? The truck maintains a constant speed of 35 m/s and does not change direction. Where does the arrow land? What is the range of the arrow?
17. A player kicks a ball at an angle of 37o with the horizontal and with an initial velocity of 15 m/s.
A second player standing at a distance of 30 m from the first (in the direction of the kick) starts running to meet the ball at the instant it is kicked. How fast must he run in order to catch the ball before it hits the ground? (4.7 m/s)
18. A football game begins with a kickoff in which the ball travels a horizontal distance of 41 m and lands on the
ground. If the ball was kicked at an angle of 40.0o above the horizontal, what was its initial speed? (20 m/s)
19. Chipping from the rough, a golfer sends the ball over a 3.00 m high tree that is 14.0 m away. The ball lands at the same level from which it was struck after traveling a horizontal distance of 17.8 m . (a) If the ball left the club 54.0o above the horizontal and landed on the green 2.24 s later, what was its initial speed) (b) How high was the ball when it passed over the tree? (13.5 m/s 4.03 m)
20. A golfer hits a ball from the origin (the tee) with an initial speed of 30.0 m/s at an angle of 50.0o above the horizontal. The ball lands on a green that is 5.00 m above the level where the ball was struck.
a. How long is the ball in the air? (4.46 s)
b. What is the ball’s range when it lands? ( 86.0 m)
c. What is the velocity when the golf ball lands? (28.4 m/s; θ = 47.1o below the horizontal)
21. Suppose a football is punted at an angle of 37.0o with a velocity of 20.0 m/s at a height of 1.00 m above the ground. How far did the football travel before hitting the ground? ( 40.5 m)
22. A shoe flung into the air such that at the end of 2.0 sec it is at its maximum height moving at 6.0 m/s. How far away will it be from the thrower when it returns to the launch altitude?
23. A baseball is hit 1.3 m above home plate. The hit send it off at an angle of 30o above the horizontal at a speed of 45 m/s. The outfield fence is 100 m away and 11.3 m high. Does the ball clear the fence?