Question
Show that when the colliding body is very-very light as compared to target and target is at rest, then colliding body rebounds with same speed.
Solution
When the two bodies collide elastically, the velocities of two bodies after collision are given by,

and
Here, we have
Therefore,
and
Thus,
Hence, we can see that the colliding body rebounds with the same speed.

and
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Here, we have

Therefore,

and

Thus,

Hence, we can see that the colliding body rebounds with the same speed.