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- Homework Statement
- The problem says that a muon with a proper lifetime of 2.2 microseconds is produced 100 km above the ground in the reference frame of Earth. We need to find the minimum speed the muon must travel that allows it to reach the ground in time before the end of its life.

- Relevant Equations
- time dilation equation: delta t from Earth frame of reference = (delta t from muon frame of reference) / Sqrt[1-(u/c)^2]

This example is worked out in the book, and at the beginning, they make the assumption that the muon is traveling at c, and then find the change in time from the Earth reference frame using delta t=100km/c. Then delta t is plugged into the time dilation equation on the left side and we solve for u. We then find that u is .999978c. My issue is I don't understand how we are able to assume that the muon was traveling at c from the beginning only to find that it was actually traveling at .999978c. Is this just an issue of approximation or is there something to the method I have misunderstood here?

This is my first post, so I'm sorry if I've done anything wrong in posting this question. I've also attached a screenshot of the problem for clarity.

This is my first post, so I'm sorry if I've done anything wrong in posting this question. I've also attached a screenshot of the problem for clarity.