Question

A particle of mass $m$ strikes a wall with a velocity $v$ making an angle $\theta$ with the wall and rebounds.The change in momentum of the particle will be :

• A. $-2m\overline{v}cos\theta$
• B. $0$
• C. $2m\overline{v}$
• D. $-2m\overline{v}sin\theta$

Answer 1

The correct option is D $-2m\overline{v}sin\theta$

the horizontal and vertical components of velocity are $vsin\theta$ and $vcos\theta$ respectively

after the collision momentum will change only in horizontal direction and not in vertical

initial momentum in horizontal direction is $m\times vsin\theta$

after collision velocity will reverse $m\times -vsin\theta$

therefore change in momentum is $\Delta p=p_f-p_i=-mvsin\theta -mvsin\theta =-2mvsin\theta$