How do I choose u' u and v for relative velocity

[grandpa2390]

Homework Statement

A certain quasar recedes from the Earth with a speed of .87c. a jet of material is ejjected towards the Earth at .55c relative to the quasar. find speed of ejected material relative to the earth

Homework Equations

u = u'+v / 1 + u'v/c^2

The Attempt at a Solution

guessing. that if I draw both reference frames, v is the velocity that stays constant. in this case v=.87c. in one reference frame, the quasar is receding, and in the other the Earth is receding from the quasar. either way there is a .87c and I will call it v.

u is the velocity in the reference frame that it is given. .55c is the velocity of the ejected material in the quasar's reference frame. I want it in the Earth's reference frame though, so I call the known velocity in the quasar's reference frame u and the unknown velocity in the Earth's reference frame u'.

and as long as I keep my signs straight, this should work right?scratch that. the signs on u and v must be from the same reference frame.

 

[Doc Al]

You might find this way of writing the velocity addition formula helpful:

Addition of (parallel) velocities:

Low-speed (Galilean) addition of velocities:
$$V_{a/c} = V_{a/b} + V_{b/c}$$

Relativistic addition of velocities:
$$V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}$$

Where $V_{a/c}$, for example, means the velocity of a as measured by c. That should allow you to keep the signs straight.