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Relative Velocities

  1. Dec 19, 2009 #1
    A approaches B at 5 MPH
    B approaches A at 5 MPH

    I am wondering why at very fast speeds, the error would become quite large if you were to say that A and B's relative velocity is equal to 10.
  2. jcsd
  3. Dec 19, 2009 #2

    Doc Al

    User Avatar

    Staff: Mentor

    I assume you mean something like this:
    A moves towards B at a speed of 5 mph with respect to some frame C.
    B moves towards A at a speed of 5 mph with respect to some frame C.

    It's a conclusion of special relativity that velocities do not add simply as V1 + V2. Read all about it: http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html" [Broken]

    (Edit: I forgot to add the punchline, that the difference becomes marked when speeds approach light speeds. DaleSpam got it.)
    Last edited by a moderator: May 4, 2017
  4. Dec 19, 2009 #3


    Staff: Mentor

    Hi ssope, welcome to PF.

    The correct formula for adding velocities is called the http://en.wikipedia.org/wiki/Velocity-addition_formula" [Broken]:

    [tex]\frac{v_1+v_2}{\frac{v_1 v_2}{c^2}+1}[/tex]

    In your case
    [tex]\frac{5+5}{\frac{5 \times 5}{(6.7 \times 10^8)^2}+1} = 9.9999999999999994 \, mph[/tex]

    For such low velocities the difference between the real formula and the approximation is undetectable, less than 1 micrometer/century.
    Last edited by a moderator: May 4, 2017
  5. Dec 19, 2009 #4
    A approaches C at 5 MPH
    C approaches B at 5 MPH
    For C: A and B's relative velocity of approach equal to 10.
    For A: the velocity of B is less than 10.
    For B: the velocity of A is less than 10.
    Last edited: Dec 19, 2009
  6. Dec 19, 2009 #5
    Thank you all very much for answering my question.
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