Question

Consider the motion of a muon as it moves through the Earth's atmosphere. After a time r = 2.20 times 10^-6 s, it decays into other particles. A particular muon is created 10,000 m above the Earth's surface and Just reaches the ground before it decays. What is the speed of the muon? (Give your answer in terms of c and to five significant figures.) 2265 c

Answer 1

$\Delta$ t_o = 2.2 X 10^-6 sec

d = 10,000 m

using equation

v = ( 1 / ( $\Delta$ t_o / d )² +1 / c² )^1/2

v = ( 1 / ( 2.2 X 10^-6 / 10000 )² +1 / ( 3 X 10⁸ )² )^1/2

v = 2.993 X 10⁸ m/sec

v = c ( approximately )