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Homework Help: Special Theory of Relativity question

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  1. Sep 4, 2012 #1
    1. The problem statement, all variables and given/known data
    I took this form Yale Open Course

    2. Relevant equations
    Special Relativity equations


    3. The attempt at a solution
    I will try to divided this problem into two parts: First one is - what is its location
    in my frame when it ticks 1 second in its frame?
    and second one - If it emits alight pulse at that time, at what time t^∗ according to me will that pulse reach my origin?.

    So for the first one i have x=? and that t'=1. I use the lorentz transformation for x point.
    x=(x' + ut')/SQRT(1-(u^2)/(c^2)). I am not sure that i can use this formula for this purpose
    but if i assume that x' is 0 i get x= ut'/SQRT(1-(u^2)/(c^2)) = 2.25 * 10^8 m
    Then i need to find t when light hits my origin ie t^* = t + t'' where t'' is time light takes to travel to my origin in my frame. Perhaps i can get t buy manipulating lornetz equation for t'. Since i have t' and x i can figure out t. t' = (t - (ux/c^2))/SQRT(1-(u^2)/(c^2)) ==>
    1 = (t - (ux/c^2))/0.8 ==> 0.8 + 0.45 = t = 1.25. So then i need to find t''. I have no idea to how to find t'' unless to plug int into standard v=s/t formula. If that's the case then c=x/t ==>
    t= 0.75 where x is 2.25 * 10^8 m which i found in first part of the problem. So t^* is 2.

    I have a feeling that i made a mistake somewhere, possibly at the beginning of the problem where i assumed that x= ut'/SQRT(1-(u^2)/(c^2)) and i am not sure if that's quite right.
     
  2. jcsd
  3. Sep 4, 2012 #2

    Janus

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    Looks good to me.
     
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