posted by Deforest .
A projectile of rest mass M1, total energy E1, and momentum p1, is directed at a stationary target of mass m2. Find the the velocity of the centre-of-momentum frame .
The total energy of a system is given by:
E = gamma m c^2
The total momentum is:
p = gamma m v
The ratio p/E is thus:
p/E = v/c^2
So, if we know the energy and momentum of a system, we know the velocity.
For the given system, the energy is:
E = E1 + m2 c^2
The momentum is
p = p1
v = c^2 p/E = c^2 p1/(E1 + m2 c^2)