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A ball at rest is dropped from a height of 12 m. It loses 25% of its kinetic energy in striking the ground, find the height to which it bounces. How do you account for the loss in kinetic energy ?

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The height from which the ball falls gives it a potential energy which converts to kinetic energy as the ball falls down. When the ball finally hits the ground, all the potential energy has converted to kinetic energy. If we assume mass of ball as M kg, then

Mgh = (final kinetic energy)

120M = (final K.E.)

Ball loses 25% of (final K.E.), so initial energy with which it bounces back = 75% of (final K.E) 

= (3/4) × 120M = 90M.

90M = Mgh

H= 9 metres.

There was a kinetic energy loss because you know, when the ball will bounce it'll create some sound and heat and vibrations on the floor, so the 25% of kinetic energy is lost there.

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