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## Homework Statement

In a given inertial frame two particles are shot out simultaneously from a given point with equal speeds

*u*at an angle of 60 degrees with respect to each other. Using the concept of 4-velocity or otherwise, show that the relative speed of the particles is given by

##u_R = u(1-3u^2/4c^2)/(1-u^2/2c^2)##

I have tried this a number of ways but always end up getting

##u_R = u(1-3u^2/4c^2)##

So I guess my question is which answer is correct?

## Homework Equations

##u'_x = (ux-v)/(1-v*ux/c^2)## and ##u'_y = uy/\gamma(1-v*ux/c^2)##

## The Attempt at a Solution

[/B]

I set S' as the stationary state of particle A, moving at a velocity u in the x direction. This meant that particle A was at rest in this frame. Therefore the velocity of B in the S' frame is the relative velocity of the two particles.

For particle B I obtained:

##u'_x = -u/2## and ##u'_y = usin60/\gamma##

Then using those values calculated the relative velocity to be

##u_R = u(1-3u^2/4c^2)##

I apologise for the layout of the equations because it is my first time posting.

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