Question

A ball strikes a wall with a velocity $\overrightarrow{u}$ at an angle θ with the normal to the wall surface and rebounds from it at angle β with the surface. Then :

• A. (θ+ β) > 90⁰, if wall is smooth
• B. If the wall is smooth, coefficient of restitution =$\frac{\tan\beta}{\cot\theta}$
• C. If wall is smooth, coefficient of restitution <$\frac{\tan\beta}{\cot\theta}$
• D. None of these

Answer 1

Answer: (B)

If the wall is smooth, coefficient of restitution =$\frac{\tan\beta}{\cot\theta}$

Answer 2

Velocity v cos β = u sin θ . . . (i)

vsin β = e. u cos θ . . . (ii)

from the above equation, tan β = e cot θ

or tan β = e tan (90⁰ - θ).

But β (90 - θ)

or (β + θ) 90⁰ From equation (ii)

e = $\frac{\tan\beta}{\tan\theta}$, Hence, (2) is the correct choice