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Special relativity homework question time dilation

  1. Nov 14, 2011 #1
    Special relativity homework question time dilation
    1. The problem statement, all variables and given/known data
    You are a passenger on a brand-new spaceship that travels at 95% of the speed of light, i.e.,
    v = 0.95 × c. The spaceship is bound for the star, Altair, at a distance of 17 light years from
    Earth. If the spaceship departs on your 21st birthday, at a speed of v = 0.95c, how old are you
    when the spaceship arrives at Altair?



    2. Relevant equations
    Δtmoving = Δtrest x [square root of (1−v^2/c^2)]

    v= d/t


    3. The attempt at a solution
    I have no idea how to do this problem, in my opinion it appears to be poorly worded, I don't know if the professor means age relative to earth time or age relative to the traveling speed. This is my attempt to find a solution:

    v=d/t v=0.95c --> 0.95c= 17lightyears/ t

    t= d/ v

    t= 17ly/ 0.95 c
     
  2. jcsd
  3. Nov 14, 2011 #2

    Doc Al

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    Staff: Mentor

    They want the actual biological age of the passenger when he arrives at the destination. So it's his frame that we are interested in.

    What you found is the time the trip takes according to Earth observers. That's not quite it. What would the time be according to the spaceship?
     
  4. Nov 14, 2011 #3
    okay, I understand how to do it, so I plug what I calculated into the time dilation equation as delta t rest and calculate tmoving based on what I have given. Thank you!
     
  5. Nov 14, 2011 #4

    Doc Al

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    Staff: Mentor

    Good! That works.

    Another approach that will give you the same answer is to ask yourself: What is the distance traveled according to the spaceship? Then you can use T = D/V from the spaceship's frame.
     
  6. Nov 14, 2011 #5

    rude man

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    Homework Helper
    Gold Member

    .. and the answer is ...?
     
  7. Nov 14, 2011 #6
    the answer for tmoving is 5.6 and when you add that to the age of the passenger that is 21yrs+ 5.6 yrs= 26.6 yrs old when the ship arrives at Altair!
     
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