Two bodies and one centre of mass

Two balls are thrown at the same moment from the same point: $A$ ($2.0\ \text{kg}$) and $B$ ($3.0\ \text{kg}$), at different velocities. Each follows its own parabola. You will make the program follow both, and their centre of mass, and find the centre of mass's own starting velocity.

The idea. Each ball: $x = u_xt$, $y = u_yt - \tfrac12 gt^2$. The centre of mass is the mass-weighted average of the two positions, and it moves like one ball thrown with $\vec{v}_{cm} = \dfrac{m_A\vec{u}_A + m_B\vec{u}_B}{m_A + m_B}$.

Your tasks.

1. Work out the positions of both balls at every time.
2. Work out the centre of mass's position at every time.
3. Work out the centre of mass's starting velocity, vx_cm and vy_cm.