Answer
The distance traveled in the lab frame is 6.0 km
Work Step by Step
We can find the distance traveled according to the muon:
$L = v~t$
$L = (0.994)(3.0\times 10^8~m/s)(2.2\times 10^{-6}~s)$
$L = 656~m$
We can find the distance $L_0$ traveled in the lab frame:
$L = L_0~\sqrt{1-\frac{v^2}{c^2}}$
$L_0 = \frac{L}{\sqrt{1-\frac{v^2}{c^2}}}$
$L_0 = \frac{656~m}{\sqrt{1-\frac{(0.994~c)^2}{c^2}}}$
$L_0 = 6000~m = 6.0~km$
The distance traveled in the lab frame is 6.0 km
