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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 railenter image description here

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?

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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 $m_1 \ge m_2$.

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