Question

An object of $mkg$ with speed of $\nu m{s}^{-1}$ strikes a wall at an angle $\theta$ and rebounds at the same speed and same angle. Find the magnitude of change in the momentum of object:

• A. $mv\sin \theta$
• B. $2mv\cos \theta$
• C. $mv\cos \theta$
• D. $2mv\sin \theta$

Answer 1

The correct option is B $2mv\cos \theta$

Let the object strikes the wall at an angle $\theta$.

Momentum when object hits ball is $p_1=mv\sin \theta \hat{i}-mv\cos \theta \hat{j}$

when it rebounds at same speed & same angle, $p_2=mv\sin \theta \hat{i}+mv\cos \theta \hat{j}$

Change in momentum $=p_2-p_1$

$=mv\sin \theta \hat{i}+mv\cos \theta \hat{j}-(mv\sin \theta \hat{i}-mv\cos \theta \hat{j})$

$\Delta \overrightarrow{p}=2mv\cos \theta \hat{j}$

$\hat{j}$ is the unit vector along $y-$ direction.

Magnitude of $\Delta \overrightarrow{p}=2mv\cos \theta$