1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Time dilation problem

  1. Nov 13, 2012 #1
    The distance to Alpha Centauri is 4,3 light years. How fast would a space ship have to travel to get there in 10 years, according to the crew?

    The answer *should* be 0,395c. So far I've gotten all sorts of answers but not much close, so I seem to be approaching the problem the wrong way.
  2. jcsd
  3. Nov 13, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Show what you've done so far.

    Hints: What's the basic idea of time dilation? What's the definition of velocity?
  4. Nov 13, 2012 #3
    The first part of the assignment asks for the time required when traveling at 30% of light speed. Given a gamma factor of 1,048 I get ~13,7 years, which is correct (so the gamma factor must be correct as well).

    velocity = distance / time


    for t = 10 and d = 4,3

    v = 4,3 / 10
    v = 0,43, which is wrong

    taking length contraction into account gives

    4,3/1,048 = 4,1

    v = 4,1 / 10
    v = 0,41, which is still wrong
  5. Nov 13, 2012 #4

    Doc Al

    User Avatar

    Staff: Mentor

    Good. Keep going.

    From Earth's viewpoint, you have the distance. What's the time?
  6. Nov 13, 2012 #5
    Hmm... i don't know. :/

    The distance is 4,3 ly but I don't know the speed, so how do I find the time?
  7. Nov 13, 2012 #6
    Hang on... the time for the crew is 10 years so the time for the observer is t/gamma

    10/1,048 = 9,54 years

    Edit: no that's not right....... I have no idea what I'm doing

    Edit2: the time from earths viewpoint is d * gamma = 4,3 * 1,048 = 10,48 years, while the time is 10 years for the crew
  8. Nov 13, 2012 #7

    Doc Al

    User Avatar

    Staff: Mentor

    You have that reversed. If the ship time is 10 years, then to earth observers it will be longer: t*gamma, not t/gamma.

    In addition to what I already pointed out, do not use the gamma from the previous part of the question.

    So continue with that velocity equation, v = d/tearth.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook