1. The problem statement, all variables and given/known data The muon is an unstable elementary particle that decays via a weak-force interaction process into an electron and two neutrinos. The life time of muons in their rest frame is 2:197 s 2:197106 s. Nuclear reactions in the upper atmosphere, precipitated by the impact of highly energetic cosmic rays, generate fast-moving muons about 10 km above sea level. Some of these particles are detected in labs at about sea level. This is possible because the life time of muons moving with respect to the Earth's surface is dilated. (i) Estimate the muons' speed relative to Earth from the fact that they travel 10.0 km between their point of creation in the atmosphere until seen to decay in ground-based labs. (ii) The proper distance travelled by the muons considered in part (a) is 10.0 km. Calculate the length of this distance as it would be measured in the muons' rest frame. Explain how your result, if interpreted using Galilean relativity, would be at odds with nding cosmic-ray muons at the Earth's surface. 2. Relevant equations gamma = 1/SQRT(1-v^2/c^2) Time = gamma*proper time 3. The attempt at a solution Honestly I'm clueless. I am really struggling with relativity but here's my current understanding of the problem (i). The muon is travelling at high speeds so it experiences time dilation and is able to travel to the surface of the earth without decaying. The proper time would be the time as measures on the Earth as it is, for all purposes, at rest right? I'm having trouble understanding the whole dilation aspect... If the partical experiences time dilation does that mean it's only undergone that time above to travel 10KM? Wouldn't that mean it was travelling faster than c? Is the 2.197x10-6 the proper time or the dilated time? :| Sorry I really don't know where to start.