Question

A ball of mass $10$ $\text{kg}$ moving with a velocity $10\sqrt{3}$ $\text{m/s}$ along the x-axis, hits another ball of mass $20$ $\text{kg}$ which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y-axis with a speed of $10\text{m/s}$. The second piece starts moving at an angle of ${30}^{\circ }$ with respect to the x-axis. The velocity of the ball moving at ${30}^{\circ }$ with x-axis is $v_2$ $\text{m/s}$. The configuration of pieces after collision is shown in the figure below The value of $v_2$ to the nearest integer is $\left(\text{in m/s}\right)$.

Answer 1

Before collision:
In x - direction
$P_i=10\times 10\sqrt{3}+20\times 0$
$P_i=100\sqrt{3}\text{kgm/s}$
Initial momentum is along x-axis only.

After collision:
Since $20\text{kg}$ ball is divded equally, so each half will have mass equal to $10\text{kg}$.
In $x-$direction:
$P_{f\left(x\right)}=10\times v_2\cos {30}^{\circ }$

Apply momentum conservation in x-direction:
$P_i=P_{f\left(x\right)}$
$100\sqrt{3}=\frac{10\sqrt{3}}{2}{v}_2$
$v_2=20\text{m/s}$
So, answer is $v_2=20\text{m/s}$