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

  1. Mar 26, 2015 #1


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    Gold Member

    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations
    u = u'+v / 1 + u'v/c^2

    3. 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: Mar 26, 2015
  2. jcsd
  3. Mar 26, 2015 #2

    Doc Al

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    Staff: Mentor

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