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Pion Decay and Relativity Question

  1. Jul 28, 2012 #1
    1. The problem statement, all variables and given/known data
    42. If a charged pion that decays in 10−8 second in its own rest frame is to travel 30
    m in the laboratory before decaying, the pion’s speed must be most nearly
    (A) 0.43 × 108 m/s
    (B) 2.84 × 108 m/s
    (C) 2.90 × 108 m/s
    (D) 2.98 × 108 m/s
    (E) 3.00 × 108 m/s


    2. Relevant equations
    Time dilation and length contraction formula? They are not given though..


    3. The attempt at a solution

    I tried to use the time dilation formula and I think that for the observer (me), the time I think the pion is experiencing should be 8.6*10^-8s and when i use this to find the speed, which is 30/t, where t is the dilated time, i get a speed more than the speed of light which is false! I am stuck at this lol. Have I used any wrong formula to calculate the speed? (That is, for relativistic speeds, I shouldn't use 30/t?) If so, which equation should I use? Thanks! I hope you can help me with this question as I would be attending a local junior olympiad soon, I am in year 10 now.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 28, 2012 #2
    By the way, the answer is D but I don't know why. Please enlighten me! Thanks.
     
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