How Do You Calculate Relative Speed of Particles Moving Orthogonally in Physics?

[pinky86]

I'm having trouble picturing the following problem.

In a given inertial frame, two particles are shot out simultaneously from a given point, with equal speed u, in orthogonal directions.

a) Without using 4-vectors show that the speed of each particle relative to the other is given by:

Ur=u*[2-{(u^2)/(c^2)}]^0.5

 

[Doc Al]

Call the given frame S'. In that frame, imagine that one particle (B) is moving with velocity +u along the y-axis; the other particle (A) is moving with velocity -u along the x-axis.

Now view things from the frame of particle A, which you can call S. Note that S' moves with speed +u along the x-axis in frame S. (The usual set up for Lorentz transformations.)

How do velocities transform in special relativity?