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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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Verified Answer
The correct answer is:
$\left(\frac{1+e^2}{1-e^2}\right) h$
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.
$H=h+2 h_1+2 h_2+2 h_n+\ldots$
$H=h+2 h e^2+2 h e^4+2 h e^6+2 h e^8+\ldots$
$=h+2 h\left(e^2+e^4+e^6+e^8+\ldots\right)$
$=h+2 h\left[\frac{e^2}{1-e^2}\right]$
$=h\left[1+\frac{2 e^2}{1-e^2}\right]$
$=h\left[\frac{1+e^2}{1-e^2}\right]$
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