Relativity?

A mu-meson moves, as measured in the system S, at speed v= c/1.06 and from its creation to its decay it travels L = 3.0 km. Calculate the proper lifetime of the mu-meson (in ns) .|||Huh?|||"proper lifetime" in this case means the lifetime of the muon measured in a the rest frame of the muon.





first, calculate the lifetime in a reference fame moving at v=c/1.06 relative to the muon.





t = L/v = (3.0*10^3 m)/(3.00*10^8 m/s /1.06)


= 1.06*10^-5 s





to transform this time into the time measured by an observer traveling in the rest frame of the muon, use the relationship





t = gamma*t0


where gamma is the Lorentz factor


gamma = 1/sqrt( 1 - (v/c)^2 )


and t0 is the "proper lifetime" of the muon





t0 = sqrt( 1 - (1/1.06)^2) * 1.06*10^-5 s


= 3.52*10^-6 s


= 3.52*10^3 ns


(1 ns = 1*10^-9 s)|||really..? here?