Velocity of the centre of mass of two photons

[Fek]

Homework Statement

Find the velocity of the centre of mass of two photons with different energies (they happen to be approaching).

Homework Equations

E = hf p(photon) = E/C E=gamma(mc^2)

The Attempt at a Solution

I have calculated the energy of the two photons in the centre of mass frame (using conservation of 4- momentum) and also the momentum of the centre of mass. However I have no idea how to get a velocity out of this.

Thank you.

 

[mfb]

How does the momentum of the center of mass look like in our lab frame?
If you know energy and momentum of that frame, you can calculate the corresponding velocity - it is like a particle at rest in this frame.

 

[I like Serena]

Welcome to PF, Fek!

From the definitions of 4-momentum and 4-velocity:

P=(E/c,p)
P=mU
U=γ(c,v)

Furthermore, for a photon we have:
E=pc

Can you deduce v from this?