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

  • #1
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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.
 
Last edited:

Answers and Replies

  • #2
Doc Al
Mentor
44,944
1,206
You might find this way of writing the velocity addition formula helpful:
Addition of (parallel) velocities:

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

Relativistic addition of velocities:
[tex]V_{a/c} = \frac{V_{a/b} + V_{b/c}}{1 + (V_{a/b} V_{b/c})/c^2}[/tex]
Where ##V_{a/c}##, for example, means the velocity of a as measured by c. That should allow you to keep the signs straight.
 

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