The following question gave a little grief:

Two smooth spheres of masses and respectively lie on a smooth horizontal table.

The spheres are projected towards each other with speeds and respectively.

i. Find the speed of each sphere after the collision in terms of , the coefficient of restitution

ii. Show that the spheres will move in opposite directions after the collision if .

My contention is that the question erred in not specifying that the answers to part i. were to be in terms of *and *.

*Solution: *

i. The following is the situation:

Let and be the velocities of the smaller respectively larger sphere after collision. Note that the initial velocity of the larger sphere is *minus *.

Using conservation of momentum,

.

Using:

,

Therefore,

,

and so

,

.

.

ii. . If and so

;

that is the particles move in opposite directions.

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