Question

A boy, standing inside a box sliding on a smooth inclined plane, throws a ball and catches it back at the same level. The unit vector along the velocity of the ball with respect to the box velocity will be

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

Answer 1

The correct option is A $\hat{j}$


For catching the ball, the boy standing inside the sliding box should not give any velocity to the ball with respect to the box in $\text{x-direction}$.i.e.,

$V_{ball/box}\hat{i}=V_{ball/ground}\hat{i}-V_{box/groung}\hat{i}=0[\because {\overrightarrow{V}}_{ball/ground}\hat{i}={\overrightarrow{V}}_{box/groung}]$

So, unit vector of velocity with respect to box should only be in $\text{y-direction}$.i,e, $\hat{j}-$ direction.

Hence, $\left(A\right)$ is the right answer.