Question

A ball is moving with a velocity of $8\text{m/s}$ towards a surface which is also moving in a downward direction with velocity of $2\text{m/s}$ as shown in figure. After collision with the surface, ball rebounds back. If the coefficient of restitution is $e=0.5$, find the rebound velocity of the ball. (Given:Velocity of surface will be same even after collision and all other external forces are absent.)

• A. $5\text{m/s}$
• B. $1.5\text{m/s}$
• C. $1\text{m/s}$
• D. $0.5\text{m/s}$

Answer 1

The correct option is C $1\text{m/s}$


Given:
Taking downward direction as negative
$u_1=-8\text{m/s},u_2=-2\text{m/s}$
$v_2=u_2=-2\text{m/s}$

Coefficient of restitution $\left(e\right)=\frac{\text{velocity of separation}}{\text{velocity of approach}}$
$e=\frac{v_2-v_1}{u_1-u_2}$
$0.5=\frac{(-2)-v_1}{(-8)-(-2)}$
$v_1=1\text{m/s}$

The rebound velocity of ball $1\text{m/s}$ in upward direction.
The correct option is (c)