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.