Question

A tennis ball hits the floor with a speed $v$ at an angle $\theta$ with the normal to the floor. If the collision is inelastic and the coefficient of restitution is $\epsilon$, what will be the angle of reflection?

• A. $ta{n}^{-1}\left[\frac{tan\theta }{\epsilon }\right]$
• B. $si{n}^{-1}\left[\frac{sin\theta }{\epsilon }\right]$
• C. $\theta \epsilon$
• D. $\theta \frac{2\epsilon }{\epsilon +1}$

Answer 1

The correct option is A $ta{n}^{-1}\left[\frac{tan\theta }{\epsilon }\right]$


Along horizontal direction momentum is conserved,
$vsin\varphi =usin\theta$___(1)
Along the vertical,
$\epsilon =\frac{vcos\varphi }{ucos\theta }=\left(\frac{sin\theta }{sin\varphi }\right)\left(\frac{cos\varphi }{cos\theta }\right)\epsilon =\frac{tan\theta }{tan\varphi }tan\varphi =\frac{tan\theta }{\epsilon }$
$\Rightarrow \varphi =ta{n}^{-1}\left[\frac{tan\theta }{\epsilon }\right]$