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Velocity of relativistic spaceship

  1. May 18, 2014 #1
    1. The problem statement, all variables and given/known data
    A spaceship travels from Earth to a star that is 6 light years away. The spaceship takes 2.5 years to reach the star in its frame. Calculate the velocity of the spaceship.


    2. Relevant equations
    [itex]x=\frac{x_0}{γ}[/itex], [itex]t=γt_0[/itex]


    3. The attempt at a solution
    I guess I have to relate the two equations to work out velocity somehow. Previous attempts where I considered the distance, [itex]6ly[/itex] divided by the velocity of the spaceship was equal to the time it takes to travel to the star as seen on Earth. I then substituted [itex]t[/itex] for [itex]γt_0[/itex] where [itex]t_0=2.5y[/itex] and rearranged to find [itex]v[/itex], but this was unsuccessful. I don't have any other ideas to try so hints would be appreciated.
     
  2. jcsd
  3. May 18, 2014 #2

    mfb

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    Staff: Mentor

    Your approach looks good. Please show your work so we can see where the calculations went wrong.
     
  4. May 18, 2014 #3
    [itex]\frac{6}{v}=t=2.5γ[/itex] where the velocity is a fraction of c, 6 is in light years and t, 2.5 are in years.

    Implies:

    [itex]\frac{6}{2.5}=\frac{v}{\sqrt{1-\frac{v^2}{c^2}}}[/itex]

    [itex]∴v=\frac{12c}{\sqrt{25c^2 + 144}}=2.4[/itex] solved with wolfram because tired

    Can't understand why I get 2.4c as an answer?
     
  5. May 18, 2014 #4
    That should be: [itex]\frac{6c}{v}=t=2.5γ[/itex]

    Chet
     
  6. May 18, 2014 #5
    Cheers
     
  7. May 18, 2014 #6

    mfb

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    Staff: Mentor

    $$\frac{6}{2.5}=\frac{v}{\sqrt{1-\frac{v^2}{c^2}}}$$
    This has a solution with v smaller than 1.

    $$∴v=\frac{12c}{\sqrt{25c^2 + 144}}=2.4$$ Don't use c here (or plug in 1), as you worked with years=speed of light = 1 anyway.

    A proper calculation with units would not have this issue...
     
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