# Vertical Motion

Try this problem, useful for Physics Olympiad based on Vertical Motion.

The Problem: Vertical Motion

A boy is standing on top of a tower of height 85m and throws a ball in the vertically upward direction at a certain speed. If 5.25 secs later he hears the ball hitting the ground, then the speed with which the boy threw the ball is ( take g=10m/s2, speed of sound in air=340m/s)
(A)    6m/s
(B)    8m/s
(C)    10m/s
(D)    12m/s

Solution:

Time taken by sound= (\frac{85}{340})=0.25secs
Time taken by the ball= 5.25-0.25=5s
Now,
Let us assume that the ball is thrown upwards with a velocity u. We know, (s=ut+\frac{1}{2}gt^2) where s is the distance covered,u is the initial velocity, g is the acceleration due to gravity and t is the time taken. Here, time taken t=5. Since the ball is thrown upwards, we have $$85=-5u+\frac{1}{2}\times10\times25$$
Hence, u is 8m/s.

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