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Special Relativity

  1. Sep 8, 2007 #1
    1. The problem statement, all variables and given/known data

    Two rocket ships, each with a rest length of 100 meters. Rocket 1 is at rest in frame S and has nose at x=0, tail at x = +100 meters. Rocket 2 is at rest in frame S' and has nose at x' = 0 and tail at x'=-100 meters. Suppose S' moves with speed V in the positive x direction realtive to S. Event A synchronizes the two frames (x=x'=t=t'=0), and event B is when the tail o rocket 2 passes the nose of rocket 1 at time t=2.5 microseconds in frame S. Find the speed V...

    2. Relevant equations

    Length contraction, and the lorentz transforms.


    3. The attempt at a solution

    What I did was say that the distance rocket 2 moved as observed from the S frame was:

    [tex]x_{b}=\frac{L_{0}}{\gamma}[/tex]

    Then the velocity would be distance over time, or:

    [tex]v=\frac{\frac{L_{0}}{\gamma}}{t_{B}}[/tex]

    Then I solve for v and get something like .133c for my relative velocity...
    Am I on the right track here?
     
  2. jcsd
  3. Sep 8, 2007 #2

    learningphysics

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    EDIT: Yes, you're right.
     
    Last edited: Sep 8, 2007
  4. Sep 8, 2007 #3
    Awesome, thanks!... while you're here, the second part of the problem states that event C is the event that the nose of rocket 2 passes the tail of rocket 1 and asks for the time coordinate with respect to the S frame...

    I'm thinking that I can just take the length of the ship (100 m) and divide by the relative velocity... but it seems too simple...
     
  5. Sep 8, 2007 #4

    learningphysics

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    Yes, that will give you the answer. BTW I get 0.132c for part 1.
     
    Last edited: Sep 8, 2007
  6. Sep 8, 2007 #5
    Sorry, yeah, I end up with .132254c also.

    Great... maybe I'm not as confused about this as I feel sometimes. I tend to think myself into circles with relativity...

    I really appreciate you taking the time to look at this with me... Thanks!
     
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