# Using rapidity - prove velocity transformation equations

1. Jul 10, 2011

### zimo

1. The problem statement, all variables and given/known data

Prove the law of transformation of velocities

$$\begin{array}{l} {v_x} = \frac{{{v_x}^\prime + V}}{{1 + {v_x}^\prime V/{c^2}}}\\ {v_y} = \frac{{{v_y}^\prime }}{{\gamma (1 + {v_x}^\prime V/{c^2})}}\\ {v_z} = \frac{{{v_z}^\prime }}{{\gamma (1 + {v_x}^\prime V/{c^2})}} \end{array}$$

2. Relevant equations

Rapidity equations

3. The attempt at a solution
I proved Vx with an ease using rapidity equations and the identity for tanh(a+b)
now, I'm stuck with revealing the relation to Vy and Vz.

2. Jul 10, 2011

### Rasalhague

What happens if you use the same method you used to prove the first equation, except taking into account that a distance in some direction orthogonal to V is the same in both coordinate systems?