Homework Help: Electron and positron length contraction q.

1. Sep 14, 2008

EngageEngage

1. The problem statement, all variables and given/known data
In the stanford linear accelerator, electrons and positrons are fired at each other at 50Gev. In the lab, each electron and positron beam is 1cm long.
(a) how long is each bundle in its frame?
(b) what is the proper length of the accelerator for a bundle to have both its ends simultaneously in the accelerator in its own reference frame.
(c) what is the length of the positron bundle in the frame of the electron bundle?

2. Relevant equations

3. The attempt at a solution
I have parts a and b completed, but for c i'm stuck. What I was thinking of doing was finding the relative speeds of the electron and positron and then using this new velocity to compute the new length contraction factor (which would be another gamma). however, it turns out that the speed of each bundle with reference to the accelerator is .999999999947c. Therefore, when I try to find their relative velocities I get the speed of light. does anyone know of another way that I could try doing this?
Thank you for any help