# Velocity Addition in Special Relativity

## Main Question or Discussion Point

Hi All,

Pardon me if this question looks so silly.

Trying to understand velocity addition in special relativity.

Say velocity components as measured in stationary frame of reference S are u, v, w in x, y, Z directions respectively and those in moving frame S' are u', v', w' in x', y', z' directions respectively. Let the velocity of relative motion between the reference frames is V and the motion is along x(or x') direction. Then velocity addition equations are as follows

u = (u'+V)/(1+(u'V/c^2)) -----(i)

v = {v'[1-(v^2/c^2)]^(1/2)}/[1+(u'V/c^2)] -----(ii)

w = {w'[1-(v^2/c^2)]^(1/2)}/[1+(u'V/c^2)] -----(iii)

Now say if light is emitted in the moving frame S' in its direction of motion x' i.e u'=c, then an observer in S measure the speed as u=c according to the equation (i)

But how do I check using eqn (ii) that light emitted in y' direction in frame S' has speed c in frame S. I substitute u'=0 and v'=c in eqn (ii), but that leads to v=c[1-(v^2/c^2)]^(1/2)