Question

A ball is moving with a speed of $4\text{m/s}$ towards a heavy wall. The wall is also moving towards the ball with velocity of $1\text{m/s}$. If the coefficient of restitution is $0.5$, find the velocity of the ball immediately after the collision. (Assume that the wall maintains the same speed even after the collision.)

• A. $3.5\text{m/s}$ along initial direction.
• B. $1.5\text{m/s}$ opposite to initial direction.
• C. $2.5\text{m/s}$ opposite to initial direction.
• D. $3.5\text{m/s}$ opposite to initial direction.

Answer 1

The correct option is D $3.5\text{m/s}$ opposite to initial direction.

Before collision

Taking velocity positive along the positive $X-$ axis and vice versa.

Given:
$u_1=4\text{m/s};u_2=-1\text{m/s}$

After collision


We know,
Coefficient of restitution, $e=\frac{\text{velocity of separation}}{\text{velocity of approach}}$
$=\frac{v_2-v_1}{u_1-u_2}\Rightarrow 0.5=\frac{-1-(-v_1)}{4-(-1)}$
$\Rightarrow v_1=3.5\text{m/s}$
$\therefore$ Velocity of the ball is $3.5\text{m/s}$ opposite to initial direction.
The correct option is (d)