Question

A ball is projected in a direction inclined to the horizontal and it bounces on a horizontal plane. If the range of first rebound is $R$ and coefficient of restitution is $e$, then range of the next rebound is

• A. $R^{\prime }=eR$
• B. $R^{\prime }=e^{2}R$
• C. $R^{\prime }=\frac{R}{e}$
• D. $R^{\prime }=R$

Answer 1

The correct option is A $R^{\prime }=eR$


As we know that,
Range $=u_x\times T$
here, $u_x$ is horizontal component of velocity
$u_x=u\cos \theta$
$u_y=u\sin \theta =$ vertical component of velocity
Time of flight, $T=\frac{2u\sin \theta }{g}$
$\Rightarrow T=\frac{2u_y}{g}$
Hence, Range $R=u_{x}T$
$\Rightarrow R=\frac{2u_x{u}_y}{g}$
After rebound, horizontal component will not change but vertical component of velocity will be decreased by $e$ times, therefore, $u_y^{\prime }=e\times u_y$
Therefore new range, $R^{\prime }=\frac{2u_x\times u_y^{\prime }}{g}$
$R^{\prime }=\frac{2e{u}_x{u}_y}{g}=e.\frac{2u_x{u}_y}{g}=eR$