The equation to determine two bodies' velocities after an elastic collision looks messy. So, it seemed like it'd be easy to derive from the conservation of momentum and the conservation of kinetic energy equations. But I spent an hour trying to derive it (well, that and watching a thing about the Black Death on Kanopy), and every time, I ended up with something with a square root in it. So, there's obviously a smoother way to derive, which I'll look up tomorrow.