In a particle physics experiment a particle called pion is used to hit a target. The particle pion has a (rest) lifetime of 2.6x 10-8 second and is accelerated to a speed 0.99c with respect to the linear accelerator. A straight beam pipe is used to transport the pions to the target. What would be the maximum length of the beam pipe? What is the length of the beam pipe the pions see?
To an observer at rest, the clock in a moving system appears to have slowed down, so that time intervals seem longer than his own clock intervals (time dilation).
[delta]t = [delta]t’/√ (1 - v^2 / c^2 )
Similarly, to an observer at rest the meter stick of the moving system appears shorter than his own meter stick (length contraction)
L = L’ *√ (1 - v^2 / c^2 )
The Attempt at a Solution
I tried to put in the numbers given and put them in the formulas but I'm not completely sure what I should do. Any help is appreciated.