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Special relativity where am I going wrong?

  1. Apr 20, 2017 #1
    1. The problem statement, all variables and given/known data
    A spaceship moves away from earth at 0.9c and fires a probe in the same direction as its motion at 0.7c. What is the probe's velocity relative to Earth?

    2. Relevant equations


    3. The attempt at a solution
    The Lorentz velocity transformation is ##v_x' = \frac{v_x - u}{1-\frac{uv}{c^2}}##, and since in this case we want to find ##v_x## this can be rearranged to get
    ##v_x = v_x' \left(1-\frac{uv_x}{c^2}\right) + u##
    So then if I substitute in numbers, I use ##v_x' = 0.7c## and ##u=0.9c##, which gives me an answer greater than the speed of light, so that's wrong.

    This is a worked example in a textbook and they've also used ##v_x'=0.7c## and ##u=0.9c## so I have no idea why that isn't working. They're using a different form of the equation, all one fraction and plus on the denominator, not ##-\frac{uv_x}{c^2}##. But then shouldn't rearranging the way I have work as well?

    The actual answer should be 0.982c. Where am I going wrong??? Did I rearrange wrong?
     
  2. jcsd
  3. Apr 20, 2017 #2
    Yes I did rearrange wrong. Missed the fact that the thing in the brackets isn't ##v_x'## so I haven't actually made ##v_x## the subject. Stupid mistake, sorry. It took me typing it up to spot that!
     
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