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## Homework Statement

A rocket is traveling at speed V along the x axis of frame S. It emits a signal (for example, a pulse of light) that travels with speed c along the y prime axis of the rocket's rest frame S prime. What is the speed of the signal as measured in S?

## Homework Equations

[tex] v_{y} = v_{y}^{'} \gamma (1-v_{x}V/c^2) [/tex]

## The Attempt at a Solution

I know the answer is C. That's readily apparent because the speed of light is constant in all inertial reference frames. But when I actually plug in the value C to this equation it doesn't give C as the answer.

From my understanding, the variables represent:

[tex] v_{y} [/tex] is the velocity of the signal relative to the S frame

[tex] v_{y}^{'} [/tex] is the velocity of the signal relative to the S prime frame

V is the relative speed between the S and S prime frames.

and [tex] v_{x} [/tex] is the velocity of the rocket relative to the S frame

So [tex] v_{y} [/tex] is what I'm solving for,

[tex] v_{y}^{'} = c [/tex]

and V is just some arbitrary speed v

Plugging in:

[tex] v_{y} = c \gamma (1-v_{x}V/c^2) [/tex]

But the rocket is at rest in S prime, so [tex] v_{x}=v [/tex]

[tex] v_{y} = c \gamma (1-v^2/c^2) [/tex]

[tex] v_{y} = c \sqrt{1-v^2/c^2} [/tex]

Where exactly am I going wrong? Am I misunderstanding the meaning behind each of the variables, or did I make some algebra error somewhere?

Thanks for the help.