Question

A ball initially at rest falls from a height $h=2.5\text{m}$. After collision with surface having value of coefficient of restitution $e=0.6$, it rebounds back. Find the rebound velocity of ball.

• A. $2\text{m/s}$
• B. $4.2\text{m/s}$
• C. $6\text{m/s}$
• D. $11.66\text{m/s}$

Answer 1

The correct option is B $4.2\text{m/s}$

Let the velocity of ball just before collision is $u_1\text{m/s}$.
We know that,
For free fall,
$u_1=\sqrt{2gh}$
$\therefore u_1=\sqrt{2\times 9.8\times 2.5}=7\text{m/s}$
Let the velocity of ball after collision be $v_1\text{m/s}$.
We know that,
$e=\frac{v_2-v_1}{u_1-u_2}$
Initial and final velocity of surface is zero
$\therefore u_2\&v_2$ are equal to zero.
$\Rightarrow e=\frac{0-v_1}{7-0}$
$\Rightarrow v_1=-e\times 7$
$\Rightarrow v_1=-0.6\times 7$
$\Rightarrow v_1=-4.2\text{m/s}$
So, the rebound velocity of the ball is $4.2\text{m/s}$.