Question

A body of mass $m$ falls from height $h$ on ground. If $e$ be the coefficient of restitution of collision between the body and ground, then the distance travelled by body before it comes to rest is

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

Answer 1

Answer: (A)

$S=h+2 e^{2} h+2 e^{4} h+\ldots$
$S=h+2 h\left[e^{2}+e^{4}+e^{6}+\ldots .\right]$
$S=h+2 h\left[\frac{e^{2}}{1-e^{2}}\right]$
Solving $S=\frac{h\left(1+e^{2}\right)}{\left(1-e^{2}\right)}$