Doubt about Relativity: Is it Possible?

[helios.jones]

Doubt about relativity!

I am a noob! Forgive me if it sounds too stupid!

Let me say, I am in CERN right now at the LHC.
I fire a proton at 0.9c in one direction. While this happens, I also fire another proton at 0.5c in the opposite direction. Both the measurements were done considering the lab as a reference frame.

The problem is, what's the speed(or velocity) of either proton relative to one another??

 

[Pengwuino]

It will be given by $v' = {{v_1 + v_2}\over{1+{{v_1v_2}\over{c^2}}}}$

Numerically either proton will see the other shoot off at .966c

Formally you consider one of the proton's rest frame and send the lab traveling off at 0.9c/0.5c and then the other proton is shot off at 0.5c/0.9c from the lab frame.