# Problem in math question

I have a sum as follows.

Two small balls of equal mass can move inside a rough endless horizontal tube of length $l$. One ball impinges with velocity $u$ on the other at rest. If the friction of the tube produces a retardation $f$ in either ball, and if after impact the balls just meet up again, prove that $2lf=(u^{2})e$ where $e$ is the co-efficient of restitution.

My problem is how can there be another collision immediately afterwards? In the sum it says if

after impact the balls just meet up again

how can the balls meet again? Have I misunderstood the sum? Any explanation will be appreciated.

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I think this question is better off in the physics stack exchange. – Ron Gordon Jan 24 '13 at 16:11
Also, the title is rather vague: most questions posted at math.se are a "problem in math question."! And ironically, this is more a "problem in physics question." – amWhy Jan 24 '13 at 16:13
No actually @rlgordonma and @ amWhhy this a Math question.. I want to know if it is possible to have an immediate collision since normally when a collision like the first happens, the velocity of the mass which moves to the same direction which had a zero velocity early would have a higher velocity than the other. Thanks in advance. – harsh Jan 24 '13 at 16:18
@harsh: even if that were true, have you thought about the units involved? Is $f$ the mass of the balls? If so, then the LHS has units of (mass)(length), while the RHS has units of (length^2)/(time^2) time whatever the units are of this coefficient (which, in my encounters with such parameters, are typically dimensionless). – Ron Gordon Jan 24 '13 at 16:21
Is this the original question, or have you translated it? – Chris Eagle Jan 24 '13 at 16:28