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

Question

A rubber ball is shot straight up from the ground with speed Vo.Simultaneously, a second rubber ball at height,h, directly abovethe first ball is dropped from rest. a. At what height above the ground do the balls collide? b. what is the max value of h for which a collision occursbefore the first ball falls back to the ground? c. for what value of h does the collision occur at the instantwhen the first ball is at its highest point a. At what height above the ground do the balls collide? b. what is the max value of h for which a collision occursbefore the first ball falls back to the ground? c. for what value of h does the collision occur at the instantwhen the first ball is at its highest point

Explanation / Answer

(a) Let the time elapsed before they meet be t.     height dropped by second ball + heightascended by first ball = h     [1/2*g*t*t] + [vo*t - 1/2*g*t*t] = vo*t =h      so, t = h/vo      so, height at which they meet = vo*t- 1/2*g*t*t = h - 1/2*g*h*h/(vo*vo) (b) time taken by the first ball to fall back toground be t.       so, v = -gt = [(-vo) -vo]          so, t = 2vo/g        For the maximum height hthe second ball must collide the first at t = 2vo/g        so, 1/2*g*t*t =1/2*g*(2vo/g)2            = h =2vo2/g (c) maximum height attained by first ball =vo2/2g = h - 1/2*g*t*t         where 0 - vo = -g*t or t = vo/g (c) maximum height attained by first ball =vo2/2g = h - 1/2*g*t*t         where 0 - vo = -g*t or t = vo/g           so, h = vo2/g

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