Relativistic velocity of probe with four reference frames

[ihearyourecho]

Homework Statement

Faraway Point starbase launches a probe toward the starships approaching from the same direction. The probe has a velocity relative to the Picard of -0.895c. The Picard approaches starbase Faraway Point with a speed of 0.795c, and the La Forge approaches the starbase with a speed of 0.895c.

A) What is the velocity of the probe relative to the La Forge?
B) What is the velocity of the probe relative to Faraway Point starbase?

Homework Equations

v₂₃=(v₂₁+v₁₃)/(1+(v₂₁+v₁₃)/c^2)

The Attempt at a Solution

Okay, this stuff really confuses me. I don't even know how to label them because there are four entities in the problem, but this equation only allows for three. Also, I'm not sure what the velocities of the Picard and the La Forge are relative to (I think to the Faraway Point?) Either way, I need a little help getting on the right path with this then hopefully I can take it from there.

I'm also not that great at the algebra of moving around the equation, but I may be able to handle that.

 

[AtticusFinch]

Your relativistic addition of velocities (I'll call it RAV from now on) formula is incorrect. This is the right one.

$$V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}$$

The speeds of the starships are given in the starbase's frame of reference. The result of RAV for Picard is given. Work backwards to find the probe's velocity relative to the starbase.

Use this result and another implementation of the RAV to find the velocity of the probe relative to La Forge.

 

[ihearyourecho]

Oh, thanks. I looked at the book too fast (I guess) when I was writing down the equation. It's not that bad at all.