# Special relativity relating S S' and S''

1. Feb 9, 2013

### Eats Dirt

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

A spaceship is moving relative to the origin S in the +z direction at say .5c and it launches an object from its frame S' at .5c in the +y direction. What is the speed of the launched object relative to S?

I think I have solved this problem correctly but am not entirely comfortable with special relativity yet.

My logic is that in the S" frame (of the launched object) it sees the earth moving at 0.5c in -z. and it also sees the earth moving at -0.5c in the -y directing at 0.5c.

This is where I am not sure. Is it correct to find the overall speed relative to S just by adding the components in quadrature?

2. Feb 9, 2013

### Dick

No, that wouldn't be correct. Suppose the speed were c and c. Adding them in quadrature would give you sqrt(c^2+c^2)=sqrt(2)c. That's greater than the speed of light. There are formulas for this sort of thing. Look at http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_case:_orthogonal_velocities

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