Question

A massive vertical wall is approaching a man at a speed $u$. When it is at a distance of $10m$, the man throws a ball with speed $10m/s$ at an angle of ${37}^{\circ }$ which after completely elastic rebound reaches back directly into his hands. The velocity $u$ of the wall is $\frac{10+x}{3}m{s}^{-1}$. Find $x$.

Answer 1

As the wall is massive, on applying conservation of momentum horizontal velocity of the ball stays constant but its direction is reversed. Also, vertical velocity of the ball remains the same.

Let the ball hits wall when wall is at a distance y from man.

$\theta ={37}^0$

Vertical velocity of the ball $=10\sin \theta =6$

Horizontal velocity of the ball $=10\cos \theta =8$

Horizontal distance covered by the ball $=2y$

Time taken by the ball to reach man's hand $=2\frac{u_{vertical}}{g}=1.2s$

$\Rightarrow 2y=8\times 1.2$

$\Rightarrow y=4.8m$

Distance travelled by the wall when ball hits wall $=10-4.8=5.2m$

$u=$ velocity of the wall $=\frac{5.2}{1.2}=\frac{13}{3}$

$\Rightarrow x=3$