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## Homework Statement

Rocket A moves with speed .75c in a northerly direction relative to an origin. Rocket B moves west (relative to that origin) with speed .4c. As B moves, it emits radiation with a wavelength 100nm normal to its line of motion, in the northerly direction. What is the wavelength of the radiation as seen by A?

## Homework Equations

Doppler shift equations

Velocity addition formulas

## The Attempt at a Solution

So far I have two different approaches to a solution, the first approach finds the wavelength of the radiation as seen by a person at the origin (which is redshifted) because the source is moving away at .4c. Then use that wavelength to find the wavelength as seen by a person moving away at .75c (to represent the rocket A). I'm not so sure about this solution...

The second idea I had was to find the relative velocity of B as seen by A (since it would be a right triangle) and using those to find the angle between the light source and the observer.

*However*, I am unsure how to find the separate components of the relative velocity. Do I keep the .75c speed in one direction and uy = uy' /(gamma(1-ux*v/c^2) to find the other direction, if that is so I have no idea what the relative velocity would be... This method is really tripping me up and I think it is the correct way. Could someone help me get on the right track?

All incite is appreciated