Answer
See explanation.
Work Step by Step
The problem asks for a speed such that the value of $\gamma$ is $\frac{1}{\sqrt{1-u^{2}/c^{2}}}=\frac{4.20\times10^{-7}s}{2.60\times10^{-8}s}=16.15$.
$u/c=\sqrt{1-(1/16.15)^2}=0.9981$
b. The lab personnel measure a distance of the pion’s speed, multiplied by its lifetime in that frame.
$d=v\Delta t = (0.9981)(3.00\times10^8m/s)( 4.20\times10^{-7}s)=126m$
