Question

A smooth sphere is moving on a horizontal surface with velocity vector $2\hat{i}+2\hat{j}$ immediately before it hits a vertical wall. The wall is parallel to $\hat{j}$ vector and the coefficient of restitution between the sphere and the wall is $e=1/2$. The velocity vector of the sphere after it hits the wall is :

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

Answer 1

Answer: (B)

$-\hat{i}+2\hat{j}$

Initial velocity of the sphere $u=2\hat{i}+2\hat{j}$

As the wall is parallel to y axis, thus its velocity componant in y direction remains the same i.e $2\hat{j}$ but its velocity componant in x direction changes.

Newtons law of collision in x direction : $\frac{-v^{\prime }-0}{v-0}=-e$

$\frac{v^{\prime }-0}{2\hat{i}-0}=-\frac{1}{2}$ $⟹v^{\prime }=-\hat{i}$

$⟹$ Velocity vector of sphere after hitting the wall $u^{\prime }=-\hat{i}+2\hat{j}$