Question

A girl throws a ball with velocity at an inclination of ${45}^o$ .The ball strikes the smooth vertical wall at a horizontal distance d from the girl and after reboundig returns to her hand. What is the coefficient o restitution between wall fand the ball .

• A. $v^2-gd$
• B. $\frac{gd}{v^2-gd}$
• C. $\frac{gd}{v^2}$
• D. $\frac{v^2}{gd}$

Answer 1

The correct option is B $\frac{gd}{v^2-gd}$

$\begin{array}{c}{t}_1+t_2=2v\frac{\sin {45}^0}{g}\\ \frac{d}{v\cos {45}^0}+\frac{d}{ev\cos {45}^0}=\frac{2v\sin {45}^0}{g}\\ \Rightarrow e=\frac{gd}{v^2-gd}\end{array}$

Hence,

option $\left(B\right)$ is correct answer.