Question

In the figure shown below, a ball is moving with a velocity of $u_1=7\text{m/s}$ in downward direction towards a surface, while the surface is moving in upward direction with a constant velocity $u_2=3\text{m/s}$. If the coefficient of restitution has value of $e=0.8$ and after collision with the surface, the ball rebounds back with velocity $v\text{m/s}$, find the rebound velocity. (Neglect all external forces)

• A. $5\text{m/s upward}$
• B. $11\text{m/s downward}$
• C. $11\text{m/s upward}$
• D. $5\text{m/s downward}$

Answer 1

The correct option is C $11\text{m/s upward}$


Given:
$u_1=-7\text{m/s},u_2=3\text{m/s},v_1=v\text{m/s}$
Taking upward direction as $+ve$
Considering surface as very heavy mass,
$\therefore$ $v_2=u_2=3\text{m/s}$
We know that:
Coefficient of restitution, $\left(e\right)=\frac{v_2-v_1}{u_1-u_2}=\frac{3-\left(v\right)}{(-7)-\left(3\right)}$
$0.8=\frac{-3+v}{10}$
$\Rightarrow v=11\text{m/s upward}$