Calculating CM Velocity in a Two-Particle System

[Tonyt88]

So I have this problem:
A mass m travels to the right at 4c/5, and another mass m is at rest.

They ask fro the energy and momentum of each particle, so I have:

Energy of traveling: 5/3 mc^2

Energy of rest: mc^2

Momentum of traveling: 4mc/3

Momentum of rest: 0

Then they ask for the velocity of the CM of the system:

Which I have 2c/5, but then some people are telling me c/2.

But anyway, I have to solve for the velocities of the particles in the CM frame, so how I do go from there.

 

[dextercioby]

What is the definition of the center of mass for a relativistic system of point particles...?

Daniel.

 

[Tonyt88]

1/M (x1m1 + x2m2) ?

 

[tim_lou]

It should be the "zero momentum" frame.

 

[Tonyt88]

Then I really don't know what to say, but I would like to know, if you have the value for the velocity at the CM (which I think is either 2c/5 or c/2), how do I go from there to solve for the resultant velocities?

 

[dextercioby]

You just need the CM's velocity. You've been hinted that in the CM frame the total momentum of the particles is zero.

Daniel.