Problem 9.13

9.13 a)
For v = .99 c, we have a $\gamma$ factor of
$\gamma = 7.09$
The time dilation equation is given by
$\Delta t = \gamma \Delta t'$
Solving for t', we have
$\Delta t' = \frac{1}{\gamma} \Delta t$
$\Delta t' = \frac{1}{7.09}(\frac{4.6 km}{.99 c})$
$\Delta t' = 2.18 \times 10^{-6}$ seconds.

b)
Similarly, the length contraction formula can be used to find the distance travelled in the muon's rest frame.
$d' = \frac{1}{\gamma} d$
$d' = \frac{1}{7.09}(4.6 km)$
d' = 649 m