Question

The mass of ball A is 10 kilograms and the mass of ball B is 5 kilograms. If the initial velocity is set to 3 meters per second for each ball, what is the final velocity of ball B if the final velocity of ball A is 2 meters per second? Use the elastic collision equation to find the final velocity of ball B. Assume ball A initially moves from right to left and ball B moves in the opposite direction. Identify each mass, velocity, and unknown. Show your work, including units, and indicate the direction of ball B in your answer.

Answer 1

During elastic collision the kinetic energy between the two colliding bodies is maintained before and after collision. In this case the initial momentum will be equivalent to the final momentum after collision. 
Therefore; M1U1 + M2U2 = M1V1 + M2V2, Where m1 and m2 are the masses of the balls respectively, u1 and u2 are the initial velocities of the two balls and v1 and v2 are the final velocities.
Thus;  (10 ×3) + (5 ×3) = (10 ×2) + (5×v2)
                                45 = 20 + 5v2
                                 25 = 5v2
                                   v2 = 5 m/s
Therefore, the final velocity of ball B will be 5 m/s  in the same direction as ball A (from right to left)