# Special relativity and velocity of a particle

1. Feb 20, 2005

### matpo39

hi, im having a little trouble figuring this problem out.

Two particles in a high-energy accelerator experiment are approaching each other head-on. Each has a speed which is f times the speed of light, as measured in the laboratory. What is the magnitude of the velocity of one particle relative to the other? Give your answer as a fraction of the speed of light.

I belive that you will have to use the lorentz velocity transformation equation which is v_1= v_2+u/(1+u*v_2/c^2) . but the answer doesnt involve u so im not sure where to go with this problem.

thanks

2. Feb 20, 2005

### Andrew Mason

The velocity of the one particle relative to the other is:

$$u = \frac{v_1 - v_2}{1 - v_1v_2/c^2}$$

Where v_2 = - v_1 = fc, you get:

$$u = 2fc/ (1 + f^2)$$

AM