Subatomic particles called muons can be created in the upper atmosphere by collisions of cosmic rays (energetic particles coming from astrophysical sources). As we shall see in a few lectures, muons quickly decay (in 2.2 microseconds on average) into other particles. Consider a muon that was created at a height the same as the top of a nearby mountain, traveled straight down towards the Earth through the atmosphere at 0.9 times the speed of light, and then decayed at a point the same height as that of a tree it reaches, after exactly 2.2 microseconds in the muon frame.

1. How fast in meters per second is the muon moving in the rest frame of someone standing on the mountain?
2. In which direction is the muon moving in the rest frame of someone standing on the mountain?
3. In the rest frame of someone standing on the mountain, how long in seconds did the muon live?
4. In the rest frame of someone standing on the mountain, and using distance equals velocity times time, find how far the muon travelled in meters.
5. In the rest frame of someone standing on the mountain, and using relativistic length contraction (that is, the muon sees a contracted mountain-tree distance), how far did the muon travel in meters?
6. True or false? The answers to the last two questions (the distance the muon traveled using time dilation or the distance traveled using length contraction) should be equal.