Question

A steel ball A of mass 20.0 kg moving with a speed of 2.0 ms−1
collides with another ball B of mass 10.0 kg which is initially at rest. After the collision A moves off with a speed of 1.0 ms−1 at an angle of 30º with its original direction of motion. Determine the final velocity of B.

Answer 1

From the conservation of momentum:

$$Mv_i=Mv_f \cos{30}+mu\cos{a}$$

$$0=Mv_f \sin{30}-mu\sin{a}$$

Thus:

$$u=v_f \frac{M \sin{30}}{m\sin{a}}$$

$$Mv_i=Mv_f \cos{30}+mv_f \frac{M \sin{30}}{m\sin{a}}\cos{a}$$

$$20(2)=20(1) \cos{30}+20(1)\sin{30}\cot{a}$$

The direction is 23.8 degrees from original direction of motion in another side from steel ball A .

The speed is

$$u=1 \frac{20 \sin{30}}{10\sin{23.8}} =2.48 m/s$$