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If a ball hits the ground with velocity 'v', it bounces back up with velocity '-v'. If such a ball is dropped from a height 'h' above the ground , how high

will it bounce? Justify you answer.



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There is no change in the magnitude of velocity after rebounding.

change in PE = change in KE  of the ball when it hits the ground
   mg h =  1/2 m v²

when the ball rebounds with  velocity v,  its initial KE = 1/2 m v²
when it reaches a height  H, its PE = m g H.
   SO using conservation of energy  m g H = 1/2 m v²
 hence  H = h.

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