Question

A ball moving in $x-y$ plane, has velocity $(4\hat{i}-4\hat{j})m/s$ just before the collision with ground. Coefficient of restitution for collision is $e=\frac{1}{2}$. What will be velocity of the ball just after the collision with ground?

• A. $(2\hat{i}+2\hat{j})m/s$
• B. $(4\hat{i}+2\hat{j})m/s$
• C. $(2\hat{i}+4\hat{j})m/s$
• D. $(4\hat{i}+4\hat{j})m/s$

Answer 1

The correct option is B $(4\hat{i}+2\hat{j})m/s$

Given,
velocity of ball before collision $=(4\hat{i}+4\hat{j})m/s$
coefficient of restitution $\left(e\right)=\frac{1}{2}$
we know that,
coefficient of restitution $\left(e\right)=\left[\frac{v_2-v_1}{u_1-u_2}\right]$
$\frac{1}{2}=\frac{v_y-0}{4-0}$
$\Rightarrow v_y=2$
$v_x$ remain same.
Hence, $v_{final}=4\hat{i}+2\hat{j}$.