Question

The velocity vector of a sphere after it hits a vertical wall which is parallel to $\hat{j}$ is $(-\hat{i}+3\hat{j})$ on a smooth horizontal surface. The coefficient of restitution between ball and wall is $\left(1/2\right)$. Find the velocity vector of sphere immediately before collision:

• A. $2\hat{i}+3\hat{j}$
• B. $-\hat{i}+\widehat{3i}$
• C. $-2\hat{i}+3\hat{j}$
• D. $\hat{i}+3\hat{j}$

Answer 1

The correct option is A $2\hat{i}+3\hat{j}$

Given:
Velocity after it hits a vertical wall which is parallel to $\hat{j}$,

$\overrightarrow{v}=(-\hat{i}+\widehat{3j})$

Therefore, as per the given question, component of velocity parallel to wall will remain unchanged. $\left(3\hat{j}\right)$ will remain same. $\left(\hat{i}\right)$ component will become

$\Rightarrow (-\hat{i})\times (-\frac{1}{e})=(-\hat{i})(-2)$

Hence,
Velocity vector of sphere immediately before collision

$=2\hat{i}+3\hat{j}$
Final answer: (d)