One particle is shot in the x direction at speed u and a second is shot in the y direction at speed u as well. Show that the relative speed of one to the other is: u(2-(u/c)^2)^1/2.
velocity addition: u = (u' +/- v)/(1 +/- u'*v)
x = [tex]\gamma[/tex](vt' + x')
y = [tex]\gamma[/tex](vt' + y')
The Attempt at a Solution
So I am getting lost when trying to go from one frame to another. Starting in the rest frame of the particle moving in the x direction (particle 1):
the speed of particle 1 is v'_x = 0 and v'_y = 0
the speed of particle 2 is v'_x = -u and v'_y = u
I do not know what to do from here to try to find the relative velocity of the two particles. Any help?