$($a$)$ How far does the muon in Example $28\mathrm{.}1$ travel according to the Earth$-$bound observer? $($b$)$ How far does it travel as viewed by an observer moving with it$?$ Base your calculation on its velocity relative to the Earth and the time it lives $($proper time$).($c$)$ Verify that these two distances are related through length contraction $=3\mathrm{.}20$$=3\mathrm{.}20.$