Lorenz velocity transformation

[ProPatto16]

Homework Statement

the particles in a high energy accelerator experiment are approaching each other head on, each with speed of 0.9520c as measured in laboratory. what is the magnitude of the velocity of one particle relative to the other?

Homework Equations

v_x = v_x' + u / 1 + (uv_x' / c²)

The Attempt at a Solution

i can't work out the variables.

the two reference frames are:
1. the lab
2. one of the particles

but that means v_x = 0.

so I am lost..

 

[tiny-tim]

Hi ProPatto16!

Using the example of http://en.wikipedia.org/wiki/Addition_of_Velocities_Formula" , one particle is the shore, the ship is the lab, and the other particle is the fly

 

[vela]

You might be getting confused because you're assuming the lab is the unprimed frame, like it usually is in other relativity problems. In this problem, though, it's the primed frame.

                       vx'
1--->        L        <---2

           u           vx
1        <---L      <-----2

 

[ProPatto16]

do you get v of particle one to particle 2 to be 0.99879c?

 

[ProPatto16]

yeah that part did catch me out. i assumed the first reference frame was lab at rest. but its actually particle 1 at rest with lab approaching at 0.9520c right?

 

[vela]

Yup, I got the same answer.

 

[ProPatto16]

thanks. i don't have the open mind i need for relativity. i just need the question set up for me than I am right