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

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Aicharya · Accepted Answer

Ball falls from height $h$ then formula for height covered by it in $n$th rebound is given by $h_n=h e^{2 n}$ where $e=$ coefficient of restitution $n=$ number of rebound Total distance travelled by particle before rebounding has stopped. $H=h+2 h_1+2 h_2+2 h_n+\ldots$ $H=h+2 h e^2+2 h e^4+2 h e^6+2 h e^8+\ldots$ $=h+2 h\left(e^2+e^4+e^6+e^8+\ldots\right)$ $=h+2 h\left[\frac{e^2}{1-e^2}\right]$ $=h\left[1+\frac{2 e^2}{1-e^2}\right]$ $=h\left[\frac{1+e^2}{1-e^2}\right]$

A ball falls from a height $h$ and rebounds after striking the floor. The coefficient of restitution is $e$.…

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