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. Which direction is the tree moving in the muon rest frame?
2. How far in meters did the muon travel in the muon's rest frame?
3. How far in meters did the tree travel in the muon's rest frame?