Collisions of different masses

A ball of mass $m_1$ at $3.0\ \text{m/s}$ hits a ball of mass $m_2$ at rest, head-on and elastically. You will make the program find both velocities afterwards for many mass ratios, and the ratio that hands over the most energy.

The idea. With $r = \dfrac{m_2}{m_1}$: $v_1 = \dfrac{1 - r}{1 + r}u$ and $v_2 = \dfrac{2}{1 + r}u$. The share of the kinetic energy that goes to the second ball is $\dfrac{r v_2^2}{u^2}$.

Your tasks.

1. Work out v1 and v2 for every ratio in r.
2. Work out the share of the kinetic energy that goes to the second ball.
3. Find the ratio that gives the second ball the biggest share.