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Law of Composition of Velocities

  1. Oct 28, 2007 #1
    1. The problem statement, all variables and given/known data

    From the relativistic law of composition of velocities one deduces that if a particle has velocity ui in O, then in a system O' moving at -vi relative to O, its velocity will be u'i where:

    u'=(u+v)/(1+(uv/c^2))

    Show, mathematically, that if 0<u<c and 0<v<c, then 0<u'<c also.

    2. Relevant equations

    Hint: Think of above equation as (u'/c)=[((u/c)+(v/c))/(1+(uv/c^2))]

    3. The attempt at a solution

    Well, I've looked at it, and figured that if 0<u<c, then 0<(u/c)<1 and the same with v and u'. However, when putting this into the form of the 'hint' equation, you'd get u'/c=(0<2)/(1<2) which would give 0<u'<2, which isn't right. I can't see where it's going wrong though. Any help?
     
    Last edited: Oct 28, 2007
  2. jcsd
  3. Oct 30, 2007 #2
    Sorry about the mess with the brackets, I couldn't get Latex to work how I wanted it!
     
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