1. Not finding help here? Sign up for a free 30min 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!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Special Relativity (Transformation question) Check Answer.
Loading...