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## Homework Statement

Mass, m

_{1}is travelling along a smooth, level track towards mass m

_{2}which is stationary. m

_{2}then strikes mass m

_{3}

All collisions are perfectly elastic, and all motion is along the same line.

Calculate m

_{2}in terms of m

_{1}and m

_{3}which results in m

_{3}having the highest possible velocity, for any given initial velocity of m

_{1}

**Attempt at a solution**

I think I have to use conservation of momentum (p=mv) and conservation of energy (E=0.5mv

^{2})

I thought I would just have to do some substitution and rearranging but after about half an hour I've gotten nowhere.

If this is what I have to do, please help me get started, if not please try to help me to understand what I have to do.

Thanks