Question

Hailstones falling vertically with a speed of 10 m s${}^{-1}$, hit the wind screen (wind screen makes an angle ${30}^o$ with the horizontal) of a moving car and rebound elastically. Find the velocity of the car if the driver finds the hailstones rebound vertically after striking.

Answer 1

For the driver to observe, the hailstones move vertically upward after the elastic collision.

Let the velocity of hailstone w.r.t care ${\overline{v}}_{h,c}$. Then

${\overline{v}}_h={\overline{v}}_{h,c}+{\overline{v}}_e$

$({\overline{v}}_h{)}_x=({\overline{v}}_{h,c}+{\overline{v}}_c$

$({\overline{h}}_h{)}_x=({\overline{v}}_{h,c}+{\overline{v}}_c{)}_x$

But $({\overline{v}}_h{)}_x=0$,since hailstones fall vertically down.

$\Rightarrow ({\hat{v}}_h{)}_x=-(v\cos {30}^o)$

$\Rightarrow |{\overline{v}}_h{|}_x=|{\overline{v}}_{h,c}{|}_x$

Now since $({\overline{v}}_h{)}_y=({\overline{v}}_{h,c}+{\overline{v}}_c{)}_y$

Since $(v_h{)}_y=-m{s}^{-1};({\overline{v}}_c{)}_y=0$

$\Rightarrow -10=-V\sin {30}^o+0$

$V\sin {30}^o=10\Rightarrow V=20m{s}^{-1}$

$({\overline{v}}_c{)}_x=V\cos {30}^o=20\times \frac{\sqrt{3}}{2}=10\sqrt{3}m{s}^{-1}$

${\overline{v}}_c=10\sqrt{3}\hat{i}m{s}^{-1}$