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Question

In the given figure all collisions are head on elastic. Then velocity of ball c after collision is 8vo3n, here n is (Answer upto two decimal places )

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Solution

After collision of ball A with ball B:
The collision being head on elastic, we can say
e=1=vA(vB)v0v0=vA+vB.......(1)
and using conservation of momentum,
mv0=2mvB+m(vA).......(2)

From (1) and (2), vB=2v03......(3)
Now ball B, with this velocity collides with ball C.
Again,
1=vC(vB)vBvB=vC+vB.......(4)
and
2mvB=2m(vB)+3mvC.......(5)

After solving equations (3), (4) and (5)
We get vC=815v0n=5

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