Question

A ball is moving with speed $3\text{m/s}$ in downward direction and the surface is moving with a constant speed of $2\text{m/s}$ upwards as shown in figure. After collision with the surface of coefficient of restitution $e=0.8$, the ball rebounds back with speed $v\text{m/s}$. Find the value of ${}^{\prime }{v}^{\prime }$. (Assume the surface doesn't change its velocity)

• A. $3\text{m/s}$
• B. $5\text{m/s}$
• C. $1\text{m/s}$
• D. $6\text{m/s}$

Answer 1

The correct option is D $6\text{m/s}$

Given,
Speed of the ball before collision $\left(u_1\right)=-3\text{m/s}$
Speed of the surface before collision $\left(u_2\right)=2\text{m/s}$
Speed of the surface after collision $\left(v_2\right)=2\text{m/s}$

Let the speed of the ball after collision $\left(v_1\right)=v\text{m/s}$

Coefficient of restitution $\left(e\right)=0.8$
We know that,
Coefficient of restitution $\left(e\right)=\frac{v_2-v_1}{u_1-u_2}$
(taking upward direction +ve)
$0.8=\frac{2-v}{-3-2}\Rightarrow v=6\text{m/s}$