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Relativity Question

  1. Jul 7, 2008 #1
    Two spaceships, each measuring 100 m in its own rest frame, pass by each other traveling
    in opposite directions. Instruments on board spaceship A determine that the front of spaceship B requires 5x10^-6 sec to traverse the full length of A.

    (a) What is the relative velocity v of the two spaceships?
    (b) How much time elapses on a clock on spaceship B as it traverses the full length of A?

    a) Well, the observer in A, in his frame, sees that B takes 5e-6 sec to go 100 m, so this means that the relative velocity, v, of the two spaceships is [tex]\boxed{100/(5 \cdot 10^{-6}) = 2\cdot 10^7 \text{m/s}}[/tex].
    1. The problem statement, all variables and given/known data

    b) We know that observer B will still observe the same relative velocity as A, by symmetry. Now, from B's reference frame, A travels at [tex]2\cdot 10^6 \text{m/s}[/tex] through [tex]100 \text{m}[/tex], so B also measures time [tex]5 \cdot 10^{-6} \text{sec}[/tex].

    Is my work above correct? Part b) seems wrong, because both measure the same time... doesn't this usually not happen?
  2. jcsd
  3. Jul 7, 2008 #2
    Ah, I think I see my mistake in part b)... there is a length contraction that B sees when A moves past, so the time isn't the same. Is this correct?
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