Question

Muons are elementary particles that have a very short lifetime of about two millionth of a second (when at rest). They can be created in the upper atmosphere (at an altitude of say 10,000 meters) by cosmic rays, in which case they travel towards the surface of the Earth at very high speeds, say 99.9% of the speed of light. If we ignored special relativity, how far could they travel at this speed before they decay? You'll notice that even though they are very fast this distance is much less than 10,000 meters, and they would never reach the ground. This is not correct however, because we know that many of these particles do reach the ground, and experiments observe them all the time. How does special relativity resolve this apparent contradiction, and how far can they actually travel before the end of their life?

Answer 1

d = 300*10^6m/s * 2*10^-6s = 600m befor decaying.