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## Homework Statement

Muons, which have a half-life of 2 x 10-6 s, are formed in the Earth's atmosphere at an

altitude of 10 km. If they travel normal to the Earth's surface, and one half of them

reach it before they decay, what is their velocity?

## Homework Equations

Lorentz Transormation.

## The Attempt at a Solution

My understanding of the question is that in the reference frame of the the muons 2 x 10-6 s elapses before they reach the surface of the Earth. So t' is 2 x 10-6 s. So I need to find out the time that elapses in the Earth's reference frame in order to calculate the relative velocity. However, the only other information I've got is x=10km (taking x to be the direction of the velocity of the muons). Aren't there too many unknowns?