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Oblique Collision

Four identica...

Question

Four identical balls. A, B, C and D are placed in line on a frictionless horizontal surface. A and D are moved with the same speed ' $u$ ' towards the middle as collisions, find the velocities.

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Solution

A and D collide especially with B and C, respectively, and come to rest but B and C starts moving with velocity $u$ towards each other as shown.
B and C collide especially and exchange their velocities to move in the opposite direction.
Now, B and C collide elastically with A and D respectively, and come to rest but A and D start moving with velocity $u$ away from each other as shown.
Therefore, final velocities. $V_{A} = u (\leftarrow), V_{B} = 0, V_{C} = 0$ and $V_{D} = u (\to)$ .

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