What is the Speed of the CM Frame in Particle Decay?

[Katie1990]

Homework Statement

A particle of mass M, traveling horizontally through the laboratory, decays into two daughter
particles, each of mass 0.4M. One of the daughters, A, is produced at rest in the Lab frame.

Show that vcm , the speed with which the CM frame moves in the Lab frame, is equal to
0.6c, and find the energy of the parent particle in the Lab frame.

Homework Equations

Conservation of 4-momentum, Relativistic energy momentum relation

The Attempt at a Solution

I have found the energys and velocities of the two daughter particles in the com frame, but am unsure how to show that Vcm is equal to 0.6c. I tried finding the energy by writing the momentum of the the stationary daughter as p1 = P - p2 and finding the square of that then rearranging to get energy but this didn't work.

 

[tiny-tim]

Hi Katie1990!

If the speed is v, what is the energy of the two 0.4M particles?

Then assuming no energy is lost, what must v be?