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Doubt & Answer Explanation

Doubt

a ball falls from a height h and rebounds after striking the floor .if coefficient of restitution is e,find the maximum distance covered before it comes to rest .


ans--( 1+e^2)h 1-e^2

Answer Explanation


When the ball touches the ground for the first time, its velocity is ?(2gh) (you can obtain this velocity by energy conservation).

After rebounding for the first time, its velocity becomes e?(2gh) upwards.


The distance covered by the ball before the first collision is h. Now, the distance covered by the ball from 1st collision to 2nd collision is 2h1 where 2h1 can be found by energy conservation.

1/2 m(e)(2gh) = mgh1

So, h1 = eh. Hence distance covered from first to second collision = 2eh.

Thus, the total distance covered after many, many collision is h + 2eh + 2e2h + 2e3h + ..... till infinity..

This is h + 2he(1+e+e2+e3+e4.... till infinity) = h + 2he/(1-e)



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