# Homework Help: Pion Decay and Relativity Question

1. Jul 28, 2012

### SecretSnow

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. Jul 28, 2012

### SecretSnow

By the way, the answer is D but I don't know why. Please enlighten me! Thanks.