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Statement of a problem № 3144

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Observed in the laboratory frame, a body of mass m1 moving at speed v col- lides elastically with a stationary mass m2 . After the collision, the bodies move at angles T1 and T2 relative to the original direction of motion of m1 . Find the velocity of the centre of mass (CM) frame of m1 and m2 . Hence show that before the collision in the CM frame m1 and m2 are approaching each other, m1 with speed m2 v/(m1 + m2 ) and m2 with speed m1 v/(m1 + m2 ). In the CM frame after the collision m1 moves off with speed m2v/(m1 + m2) at an angle T to its original direction. Draw a diagram showing the direction and speed of m2 in the CM frame after the collision. Find an expression for the speed m1 after the collision in the laboratory frame in terms of m1 , m2 , v and the angle T .

Solution:
Observed in the laboratory frame, a body of mass m1 moving at speed v col- lides

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