a ball is thrown up vertically from the ground with velocity vo and another body is simultaneously dropped from height H they meet at height h/2 if vo equals to
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Let us take the point from where the ball A is thrown upwards as origin and the upwards direction positive for ball A. The ball is thrown up with a velocity u at time t =0. It is acted upon by acceleration (-g) due to gravity. The velocity of the body at time t= t is given by
v(A) = u - g t and directed upwards–––––––––(1)
At the same instant of time t=0, another ball is dropped from top of tower. Its initial velocity = 0, and it is acted upon by acceleration (-g) due to gravity.We have taken up as positive. Its velocity after an elapse of time t=t is given by;
v(B) = - g t directed downwards.
To find the velocity of A relative to B, we need to bring B to rest by imposing on B a velocity equal to (+g t). The same velocity also needs to be imposed on A as well. Velocity of B after imposing velocity (+g t) on is zero. And the velocity of A after imposing a velocity (+g t) on it also = u - g t + g t = u
So velocity of A relative to B after a elapse of time t seconds = u and directed upwards, ie relative velocity is always u.
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