Question

A small ball of mass $m$ collide with a smooth wall, moving with constant speed $u$ at an angle $\theta$ with the normal to the wall. After collision, the ball moves at the same angle $\theta$ with the normal to the wall with the same constant speed. Find the average impulse on the ball.

• A. $2mu\cos \theta$
• B. $2mu\sin \theta$
• C. $mu$
• D. $mu(\cos \theta -\sin \theta )$

Answer 1

The correct option is A $2mu\cos \theta$


Initial momentum, ${\overrightarrow{p}}_i=mu\cos \theta \hat{i}+mu\sin \theta \hat{j}$

Final momentum, ${\overrightarrow{p}}_f=-mu\cos \theta \hat{i}+mu\sin \theta \hat{j}$

So, average impulse,

$\Delta \overrightarrow{p}={\overrightarrow{p}}_f-{\overrightarrow{p}}_i=-2mu\cos \theta \hat{i}$

$\therefore |\Delta \overrightarrow{p}|=2mu\cos \theta$

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