Question

A ball moving the velocity $\hat{i}$ collides with a stationary wall and returns with a velocity $\hat{j}/2$. The coefficient of restitution for this collision is $\frac{1}{K}$. Find the value of $K$.

Answer 1

After impact perpendicular speed $v^{\prime }=e\cos \theta$

$\frac{1}{2}\cos (90-\theta )=e\cos \theta \frac{1}{2}\sin \theta =e\cos \theta \frac{\tan \theta }{2}=e\to \left(1\right)$

Now $\sin \theta =\frac{1}{2}\sin (90-\theta )$

$\tan \theta =\frac{1}{2}\to \left(ii\right)e=\frac{1}{4},K:4$