Answer to Question #87153 in Classical Mechanics for Rinku Rai

Question #87153
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.
1
Expert's answer
2019-03-28T05:30:59-0400

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"


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