A rubber ball is shot straight up from the ground with speed v_0.Simultaneously,

Question

A rubber ball is shot straight up from the ground with speed v_0.Simultaneously, a second rubber ball at height h directly above the first ball is dropped from rest.

At what height above the ground do the balls collide? Your answer will be a symbolic expression in terms of v_0, h, and g

What is the maximum value of h for which a collision occurs before the first ball falls back to the ground?
For what value of h does the collision occur at the instant when the first ball is at its highest point?

Explanation / Answer

Let at a height "H" from ground, the balls collide

Now,

H = v0t- 0.5gt2 ............(t is the time of collision)

Also,

h - H = 0.5gt2 ...............(for ball dropped from building at height "h" and has zero initial velocity)

Solving, the 2 equations, we get,

H = v0t- (h - H)

   v0t = h

Hence, v0 = h/t

Putting its value in 1, we get,

H = h - 0.5g*(h/v0)2

Hoping that it would be useful to you to proceed further!

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