Question

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

• A. $\frac{\left(1-e^2\right)h}{e^2}$
• B. $\frac{\left(1+e^2\right)h}{e^2}$
• C. $\left(\frac{1+e^2}{1-e^2}\right)h$
• D. $\frac{e^{2}h}{1-e^2}$

Answer 1

Answer: (C)

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