Problem Set 1: Projectile Motion
Direction: Answer the following problems correctly. Show your complete solutions.
1. A stone is thrown horizontally at a speed of 5.0 m/s from the top of a cliff 78.4 m high. How long does it take
the stone to reach the bottom of the cliff? How far from the base of the cliff does the stone strike the ground?
Given: Vx = 5.0 m/s, y = 78.4m, g = โ9.8๐/๐ 2
Unknown: t, x
Solution: ๐ก = โโ2๐ฆ
๐ x = ๐๐ฅ๐ก
๐ก = โโ2(78.4๐)
โ9.8๐/๐ 2 = 4s x = 5.0๐/๐ (4๐ ) = 20ms
Answer: t = 4s, x = 20m
2. A player kicks a football from the ground level with a velocity 27.0 m/s at an angle of 300 above the horizontal.
Find its โhang timeโ, horizontal distance and its maximum height.
Given: Vo =27 m/s, ฮธ=30โ, g =9.8๐/๐ 2
Unknown: T, R=x, ๐๐๐๐ฅ
Solution: ๐ = 2๐ฃ๐๐ ๐๐๐
๐ ๐
= ๐ฃ๐๐ ๐๐2๐
2๐ ๐ = ๐ฃ๐
2๐ ๐๐2๐
2๐
๐ = 2(27๐
๐ )๐ ๐๐30ยฐ
9.8๐/๐ 2 = 2.75s ๐
= (27๐/๐ )2sin(2โ30ยฐ)
9.8๐/๐ 2 = 64.422m ๐ = (27๐/๐ )2๐ ๐๐230ยฐ
2(9.8๐
๐ 2) = 9.298m
Answer: T = 2.75s, R = 64.42m, T = 9.3m
3. A long jumper leaves the ground with an initial velocity of 10.5 m/s at an angle of 25-degrees above the
horizontal. What is the time of flight, the horizontal distance, and the peak height of the long-jumper?
Given: Vo = 10.5 m/s, =25ยฐ , 2๐ = 50ยฐ, g = 9.8๐/๐ 2
Unknown: ๐ก๐๐๐๐โ๐ก, R=x, ๐๐๐๐ฅ
Solution: ๐
= ๐ฃ๐๐ ๐๐2๐
2๐ ๐ก๐๐๐๐โ๐ก = ๐ฅ
๐๐๐๐๐ ๐ ๐๐๐๐ฅ = ๐๐๐ ๐๐๐๐กโ 1
2๐๐ก2
๐
= (10.5๐/๐ )2sin 50ยฐ
9.8๐/๐ 2 = 8.62m = x ๐ก๐๐๐๐โ๐ก = 8.62๐
10.5๐
๐ cos (25ยฐ) = 0.91s
๐๐๐๐ฅ =10.5๐
๐ ๐ ๐๐(25ยฐ)(0.46) โ1
2(9.8๐/๐ 2)(0.46)2 = 1.00m
Answer: R = x = 8.62m, ๐ก๐๐๐๐โ๐ก =0.91๐ , ๐๐๐๐ฅ = 1.00๐
4. During World War I, the Germans constructed an enormous railway gun that was used to bombard Paris from
a distance of 120 km.
