An object of mass m, projected into objects m2 and m3

[Jon.G]

Homework Statement

Mass, m₁ is traveling along a smooth, level track towards mass m₂ which is stationary. m₂ then strikes mass m₃
All collisions are perfectly elastic, and all motion is along the same line.
Calculate m₂ in terms of m₁ and m₃ which results in m₃ having the highest possible velocity, for any given initial velocity of m₁





Attempt at a solution
I think I have to use conservation of momentum (p=mv) and conservation of energy (E=0.5mv²)
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

 

[hjelmgart]

Conservation of energy or momentum is fine, whatever you prefer. Probably you can find the equation for elastic collision and conservation of momentum.
Then draw the scenario and divide it into 3 sub problems, assign the total momentum before and after each collision. Start by putting up the equations without writing m_2 in terms of the other, as this could simplify it later, and makes it easier to see, if you did it right from the start.