Non-parallel velocity addition

[jturko]

Homework Statement

A spaceship moves with a velocity 0.75c xhat with respect to the earth. The ship releases a probe with a velocity 0.75c yhat relative to the ship. What is the velocity of the probe as viewed on earth, magnitude and direction?

Homework Equations

The velocity-addition formulae for all three spatial directions

The Attempt at a Solution

I think that the velocity observed in the x direction of the probe will just be 0.75c, but I am having trouble wrapping my head around finding the velocity in the other directions. I know the velocity is changed due to the time dilation but cannot find the necessary equations to use. I think we are supposed to use 4-vectors

 

[haruspex]

Try http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_case:_orthogonal_velocities