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Homework Help: Lorentz transformation problem

  1. Mar 23, 2008 #1
    1. The problem statement, all variables and given/known data
    A spaceship has a speed of .8c relative to Earth. In its own reference fram, the length of this spaceship is 300m.
    a.) consider a light emiited from the tail of this spaceship. In the reference frame of the spaceship, how long does this pulse take to reach the nose>
    b.) In the reference frame of the Earth, how long does this take? Calculate this time directly from the motions of the spaceship and the light pulse; hen recalculate it by applying the Lorentz transformations to the result obtained in (a).

    2. Relevant equations
    [tex] t =\frac{t' + \frac{Vx'}{c^{2}}}{\sqrt{1-\frac{V^{2}}{c^{2}}}}

    3. The attempt at a solution
    I think i have part a figured out.. All i did was divide 300 by c to get [tex] \Delta t' = 1.0*10^-6s[/tex]

    b.) For this part, I cannot figure out how to do it without using the Lorentz transform directly like so:
    [tex]t' = 1.0*10^-6s........
    x' = 300m........
    V = .8c

    [tex] t =\frac{1.0*10^-6s + \frac{.8c(300m)}{c^{2}}}{\sqrt{1-\frac{(.8c)^{2}}{c^{2}}}}
    = 1.40 * 10^-6s [/tex]

    I cannot do this though without the lorentz transform. We haven't gone over length contraction yet, so I cannot use it to determine the length of the spaceship in earths reference frame. If anyone could please help me get started on this I would appreciate it greatly!
    Last edited: Mar 23, 2008
  2. jcsd
  3. Mar 23, 2008 #2
    I've been trying to manipulate the other lorentz equations ( in specific the ones for x), but i cannot find anything that will work. Once again, If someone could help me out here I would appreciate it
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