Question

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

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

Answer 1

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

The ball has a velocity $v$ in downward direction just before collision.

Its velocity component parallel to the inclined plane remains constant whereas that of perpendicular to the plane changes from $vcos\theta$ to $v^{\prime }$ after the collision.

$\frac{v^{\prime }-0}{-vcos\theta -0}=-e$ $⟹v^{\prime }=evcos\theta$

As the ball moves in horizontal direction after the collision, thus it makes angle $\theta$ with inclined plane

$\therefore$ $tan\theta =\frac{v^{\prime }}{vsin\theta }$

$tan\theta =\frac{evcos\theta }{vsin\theta }$ $⟹e=ta{n}^2\theta$