Question

A ball collides with a smooth and fixed inclined plane of inclination $\theta$ after falling vertically through a distance $h$. If it moves horizontally just after the impact, the coefficient of restitution is:

• A. $ta{n}^2\theta$
• B. $co{t}^2\theta$
• C. $tan\theta$
• D. $cot\theta$

Answer 1

The correct option is A $ta{n}^2\theta$

Let initial and final velocity of the ball be $u$ and $v$ respectively.

As velocity component along the inclined plane remains unchanged,

$vcos\theta =usin\theta ⟹\frac{v}{u}=tan\theta$

Now coefficient of restitution is, ratio of relative velocity of ball and inclined plane, after and before the collision, along the line of impact (i.e. Normal to the inclined plane).

So, $e=\frac{vsin\theta }{ucos\theta }=\frac{v}{u}tan\theta =ta{n}^2\theta$