Relativistic Effects on Muons' Probability to Reach Earth Surface

[yuvlevental]

Homework Statement

Within the system of the muon, which relavisitic effect increases the probability for the muon to reach the Earth surface?
Length contraction of the distance to Earth.
Time dilation of its mean-life.
Both of the above.
None the above, the probability is lower in the system of the muon.

Homework Equations

Its conceptual

The Attempt at a Solution

I thought it was both, but the online homework system says that length is correct. am i wrong and why?

 

[Doc Al]

Since the muon is the "clock" (its lifetime is a natural clock), what frame will see that clock slow down?

 

[Dick]

Time dilation in one frame is the same as length contraction in another frame, but not in both. Think about it. Which frame are they asking the question in?