Problem 2: The life and times of a Muon Muons have a short average lifespan of 2.2 microseconds (in their rest frame). They are created upon impact of cosmic radiation with the upper atmosphere, and then travel to the surface of the Earth where they cauld be detected. (a) (2) What is the average life span of muons ying at a velocity of 0.8c, measured by an observer on Earth? (b) (2) How long would it take for a muon moving as fast as light to traverse the 50km between the where it is created and the surface of the Earth? (c) (3) Even with relativistic time dilation enhancing the life span of muons, BBC is not fast enough for the muons to reach Earth's surface. At what velocity should the muons move in order for them to reach Earth? More specifically: Muons need to fly 50km from their point of creation to the surface of the Earth in order to be detected. What is the minimal velocity v with which the muons can move for that to be possible, assuming they only live for 2.2 microseconds? Hint: v is going to be very close to the speed of light. So you really need to find c-v. Ask yourselves how far can the muon move given its time-dilated life span. (d) (3) From the perspective of the muon moving at the velocity you found in part (c), how far did the muon appear to move relative to an observer on Earth? Namely, how far did the Earth or an observer on it seem to move during the muon's life time in the muon's frame? Hint: What is the lifetime of the muon in the muon's frame of reference