Question

A ball with a speed of $9\text{m/s}$ collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of ${30}^{\circ }$ with the original direction. The ratio of velocities of the balls after collision is $x:y$, where $x$ is

Answer 1

Let $v_1$ and $v_2$ be the speed of the balls after collision.

Momentum is conserved before and after the collision in both $x$ and $y$ direction.

In $y$ direction :
$p_i=0$
$p_f=m{v}_1\sin {30}^{\circ }-m{v}_2\sin {30}^{\circ }$

$\therefore 0=m{v}_1\sin {30}^{\circ }-m{v}_2\sin {30}^{\circ }$

$\Rightarrow 0=\frac{m{v}_1}{2}-\frac{m{v}_2}{2}$

$\Rightarrow \frac{v_1}{v_2}=\frac{1}{1}=1:1=x:y$

$\Rightarrow x=1$