Question

A small spherical ball strikes a frictionless horizontal plane with a velocity $v$ making an angle $\theta$ to the normal at the surface. If the coefficient of restitution is $e,$ the particle will again strike the surface after time:

• A. $\frac{2v\sin \theta }{g}$
• B. $\frac{2ev\cos \theta }{g}$
• C. $\frac{2ev\sin \theta }{g}$
• D. $\frac{2v\cos \theta }{g}$

Answer 1

The correct option is A $\frac{2v\sin \theta }{g}$

R.E.F image

Solution

$v^{\prime }sin\alpha =vsin\theta$

$\frac{v^{\prime }cos\alpha }{v^{\prime }cos\theta }=e$

$\Rightarrow v^{\prime }cos\alpha$ $=evcos\theta$

For finding time of light

Applying second $E{q}^n$ of motion,

$h=ut+\frac{a{t}^2}{2}$

$\Rightarrow u=v^{\prime }cos\alpha t-\frac{g}{2}{t}^2$

$\Rightarrow t=\frac{2v^{\prime }cos\alpha }{g}=\frac{2evcos\theta }{g}$

option - B is correct