Velocity Addition Formula: u_y > c?

[D O]

If a frame S' moves with velocity v in x direction wrt S, and you have v = 0.5c, u_x' = -0.9c and u_y' = 0.9c then it seems you find that u_y = 1.417c, greater than c.

The relevant formula is:

u_y = u_y'/(gamma * [1+v u_x' / c^2])

Apologies for formatting.

Details: gamma = 1/sqrt(1-v^2/c^2) = 2/sqrt(3)

 

[DrGreg]

$u_{x'} = -0.9c$ and $u_{y'} = 0.9c$ is impossible because $u_{x'}^2 + u_{y'}^2 < c^2$.

You can learn how to format equations for this forum here. It's not difficult.

 

[D O]

$u_{x'} = -0.9c$ and $u_{y'} = 0.9c$ is impossible because $u_{x'}^2 + u_{y'}^2 < c^2$.

You can learn how to format equations for this forum here. It's not difficult.

Oh, of course! Thanks