Question

A perfectly elastic ball falls freely from a height h = 2.5 m onto an inclined plane of inclination $\alpha ={37}^{\circ }$. Find the range S of the ball on the inclined plane. (See figure) (Take $g=10m{s}^{-2}$)

• A. 6 m
• B. 12 m
• C. 18 m
• D. 24 m

Answer 1

The correct option is B 12 m

The speed of the ball just before hitting the incline plane can be calculated using conservation of energy
$v^2=2gh$
The ball hits the inclined plane with speed v at an angle $\alpha$ with the normal and rebounds with the same speed at the same angle on the other side of the normal as shown in the figure.
Consider the coordinate axis as shown in the figure. The components of the velocity along and perpendicular to the inclined plane are
$v_x=vsin\alpha$
$v_y=vcos\alpha$
The components of acceleration due to gravity along and perpendicular to the incline plane are
$a_x=gsin\alpha$
$a_y=-gcos\alpha$
Let T be the time period of the projectile motion of the ball on the incline plane. Using, equation of motion, we get
$0=v_{y}T+\frac{1}{2}{a}_y{T}^2\Rightarrow T=\frac{2v}{g}$
Thus, using equation of motion, we get
$s=v_{x}T+\frac{1}{2}{a}_x{T}^2=\frac{4v^{2}sin\alpha }{g}=8hsin\alpha =12m$