Answer
See explanation.
Work Step by Step
a. $t=\frac{L}{v}=\frac{45000m}{0.99540c}=1.51\times10^{-4}s$.
b. The value of $\gamma$ is $\frac{1}{\sqrt{1-u^{2}/c^{2}}}=10.4377$.
$\mathcal{l}=\frac{\mathcal{l}_o}{\gamma}=\frac{45.0 km}{10.4377}=4311m=4.31 km$.
c. Use the time dilation formula.
$\Delta t_o=\frac{1.51\times10^{-4}s }{\gamma}=1.44\times10^{-5}s $
Or, calculate the time by using kinematics.
$\frac{L}{v}=\frac{4311m}{0.99540c}=1.44\times10^{-5}s $.
As expected, the two results agree.
