Question

A ball is dropped from height $5m$. The time after which ball stops rebounding if coefficient of restitution between ball and ground $e=1/2$, is

• A. $1sec$
• B. $2sec$
• C. $3sec$
• D. $infinite$

Answer 1

Answer: (B), (C)

The correct options are
B $2sec$
C $3sec$

Given
$h=5m$

$e=\frac{1}{2}$

Let, $t$ be the time taken by ball to fall from height $h$ and $t^{{}^{\prime }}$ be the time taken by ball to come to rest.
The time taken by ball to fall from height $h$ is

$t=\sqrt{\frac{2h}{g}}$

$t=\sqrt{\frac{\left(2\right)\left(5\right)}{10}}$

$t=1sec$
Now, the time taken by ball to come to rest is

$t^{{}^{\prime }}=t\left[\frac{1+e}{1-e}\right]$

$t^{{}^{\prime }}=\left(1\right)\left[\frac{1+\frac{1}{2}}{1-\frac{1}{2}}\right]$

$t^{{}^{\prime }}=\frac{\frac{3}{2}}{\frac{1}{2}}$

$t^{\prime }=3sec$