# What mass ratio to choose to get max distance covered after a collision?

We have two particles on frictionless rails:

S1: with Mass m1 and Velocity v1=0m/s

S2: with Mass m2 and Velocity v2

m1 >= m2

So particle S2 is moving toward particle S1 which is initially at rest with a constant speed V2

S1 and S2 collide: So the question is how can we choose a ratio m1/m2 in order to get a maximum distance L covered on the rail

Knowing that: $$L= \frac{4m_{2}^{2}V_{2}^{2}}{g(m_{1}+m_{2})^2}$$

The answer is 1 but i just don't understand why?

In the expression for $L$, divide numerator and denominator by $m_2^2$. Then choose a value for $\frac{m_1}{m_2}$ which makes the denominator as small as possible, subject to the condition $m_1 \ge m_2$.