Muons are created in the atmosphere by collisions of cosmic rays (mostly high energy protons) with air molecules. Muons have a rest energy of 105.7 MeV and a half life in the laboratory frame of 1.4μs. This lifetime can be increased indefinitely by time dilation.
a) Calculate the half-life of muons travelling at a speed such that the kinetic energy is ten times the rest energy.
b) calculate the speed as a fraction of c (c = 2.998*108).
c) calculate the average distance the muons travel at this speed.