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Homework Help: Special Relativity (Transformation question) Check Answer.

  1. Apr 25, 2012 #1
    1. The problem statement, all variables and given/known data
    A boat with mast at angle θ to its deck is travelling at velocity v relative to an observer, what angle does this observer see.

    2. Relevant equations

    3. The attempt at a solution
    So by using Lorentz Transformation: x'=(x-vt)*g where g=gamma
    The mast is length 'r'' and at an angle θ' to the deck of the moving boat, so x' = r'*cos(θ')
    By substitution, r'*cos(θ') = (x-vt)g and θ' = cos-1(x-vt/r'*√(1-(v2/c2))).

    Am I right or not? Thanks
  2. jcsd
  3. Apr 25, 2012 #2
    Ah, yes, this is a very good problem, but only if you do the follow up of looking at the problem using velocities (that is to say a spotlight mounted to a boat forming an angle).

    Anyway, to get to your answer: no, sorry it's not right. You just transformed x coordinates, but length is the difference between x coordinates. The length contraction formula is actually derived through the difference in x coordinates L'=x2'-x1'=x2*g-vt*g-x1*g+vt*g=g*(x2-x1)=g*L.
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