# Time Dilation

1. May 24, 2016

### katamaster818

1. The problem statement, all variables and given/known data
An unstable particle with a mean lifetime of 4 microsecond is formed by a high-energy accelerator and projected through a laboratory with a speed of 0.6c

a. What is the mean lifetime of the particle as determined by an observer in the labratory
b. What is the average distance that the particle travels in the laboratory before decaying
c. How far does an observer at rest with respect to the particle determine its distance to be before it decays

2. Relevant equations

λ = 1 / ((1-V2/c2)1/2)
Δt = λ * Δt
Mean Lifetime = 1 / λ

3. The attempt at a solution

λ = 1 / ( ( 1 - ( (0.6) (299792458) )2 / 2997924582 )1/2 = 1.5625
Δt = λ * Δt = 1.5625 * 4 microseconds = 6.25 microseconds

According to the answers provided to us by the teacher, answer should be 5 microseconds. Where am I going wrong? Am I using the wrong equation?

Edit: This is only part A I've gotten to so far, and I'm hesitant to move on without making sure I get the first part correct.

2. May 24, 2016

### katamaster818

Figured out my problem, plugged the numbers in again, and I missed the sqrt :/ Sorry to trouble you guys!

3. May 24, 2016

### phyzguy

You just did the arithmetic wrong. 1/√(1-0.6^2) = 1/√(1-0.36) = 1/√(0.64) = 1/0.8 = 1.25