An unstable particle $($mean lifetime $=2\mathrm{.}2$s$\backslash$tau $=2\mathrm{.}2\backslash ,\backslash$mu$\backslash$text$\{$s$\}$$=2\mathrm{.}2$s$,$ mass m$=106$MeV$/$c$2$m $=106\backslash ,\backslash$text$\{$MeV$\}/$c$^2$m$=106$MeV$/$c$2)$ is created in the atmosphere at an altitude of $3\mathrm{.}0$ km$,$ as measured in the Earth's inertial frame, when cosmic radiation collides with a molecule in the atmosphere. After its creation, the particle moves towards the Earth at a speed of v$=0\mathrm{.}995$cv $=0\mathrm{.}995$cv$=0\mathrm{.}995$c$.$

a$)$ How much time does it take for the particle to reach the Earth's surface in the Earth's inertial frame? $(1$ point$)$

b$)$ How much time does it take for the particle to reach the Earth's surface in the particle's own inertial frame? $(2$ points$)$

c$)$ Can this particle be observed on the Earth's surface? $(1$ point$)$

d$)$ What is the energy of the particle as measured in the Earth's inertial frame? $(2$ points$)$

e$)$ What is the energy of the particle in its own inertial frame? $(2$ points$)$