Question

A $20g$ ball hits a wall at ${45}^{\circ }$ angle with a speed of $15m{s}^{-1}$and rebounds perpendicular to the direction of incidence with same speed. Find the impulse receive by the ball.

Answer 1

Given $m=20g$ and $v=15m/s$,

As shown in figure,

Before the particle strike,

Linear momentum perpendicular to the wall$=mvsin\left({45}^o\right)=\frac{mv}{\sqrt{2}}$

Linear momentum along to the wall$=mvcos\left({45}^o\right)$

After the particle strike,

Linear momentum perpendicular to the wall$=-mvsin\left({45}^o\right)=-\frac{mv}{\sqrt{2}}$

Linear momentum along to the wall$=mvcos\left({45}^o\right)$

Impulse=change in linear momentum,

Linear Momentum changed only perpendicular to the wall.

$\Rightarrow Impulse=-\frac{mv}{\sqrt{2}}-\frac{mv}{\sqrt{2}}=-\sqrt{2}mv=-\sqrt{2}\times \frac{20}{1000}\times 15=-\frac{3\sqrt{2}}{10}$ $Kgm/s$