Time dilation and length contraction help

[dswatson]

The average lifetime of a muon is 2.2 microsec. What is the average distance the muon would travel in free space before decaying according to a stationary observer watching the muon travel with a speed of (.60c).

I know how to find the proper time.

2.2/Sqrt[1-(.6c/c)^2] = 2.2/Sqrt[1-.6^2] = 2.2*1.25 =2.75 microsec

thank you in advance for any help.

 

[Lyuokdea]

Once you've found the proper time you're basically done. You don't have to worry about length contraction in this case because the observer isn't traveling at any speed. The objects agree on how fast they are traveling with respect to each other.

~Lyuokdea

 

[turin]

It also may be instructive to draw a 1+1 D space-time diagram and see what is the x-value after you shift to the appropriate point on the hyperbola.