Question

A muon travels $60km$through the atmosphere at a speed of $0.9997c$.According to the muon, how thick is the atmosphere?

Short answer

The atmosphere is $1.5km$thick.

Step-by-step solution

Given Information

We have given that, a muon travels $60km$through the atmosphere at a speed of$0.9997c$.

Simplify

The correct length of the atmosphere in this scenario is $60km$.

For length contraction, use the following formula:

$L=\frac{L_{\rho }}{\gamma }$

$$\begin{gathered} =L_{\rho }\sqrt{1-\frac{v^2}{c^2}} \\ =(60km)\sqrt{1-{(0.9997)}^2} \\ =1.5km \end{gathered}$$

Therefore, according to the muon, the atmosphere is $1.5km$thick.