1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Dale

    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
    Hi,
    A approaches C at 5 MPH
    C approaches B at 5 MPH
    Then
    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.
    Regards.
     
    Last edited: Dec 19, 2009
  6. Dec 19, 2009 #5
    Thank you all very much for answering my question.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Relative Velocities
  1. Relative velocity (Replies: 9)

  2. Relative velocity (Replies: 6)

  3. Relative velocity (Replies: 1)

Loading...