A ball is dropped on a smooth inclined plane and is observed to...

A ball is dropped on a smooth inclined plane and is observed to move horizontally after the impact. The coefficient of restitution between the plane and ball is

e

. The inclination of the plane& is

Options

A ${45}^{o}$
B $\tan^{-1} e$
C $\tan^{-1}\sqrt{e}$
D $\tan^{-1}\dfrac{e}{2}$

Correct answer

C. $\tan^{-1}\sqrt{e}$

Step-by-step solution

Along the inclined plane

$musin\theta = mvcos\theta$

$⇒ tan\theta = \dfrac{v}{u}$

Now, $e = - \left[\dfrac{{v}_{2} - {v}_{1}}{{u}_{2} - {u}_{1}}\right] $ = - \left[\dfrac{0 - \lleft(-vsin\theta\right)}{0 - ucos\theta}] $ $ \tan^{2} \theta =e $$ \theta = \tan^{- 1}\sqrt{e}

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