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The solution assumes a speed of 3.00 EMuons are elementary particles with a (proper) lifetime of 2.2us. They are produced with very high speeds in the upper atmosphere when cosmic rays (high-energy particles from space) collide with air molecules. Take the heigh L_{0}of the atmosphere to be 100km in the reference frame of the Earth, and find the minimum speed that enables the muons to survive the journey to the surface of the Earth.

^{8}m/s to calculate Δt=333us since it traveled 100km.

Next, 333us and 2.2us is used to solve for velocity using the time dilation formula. Velocity is reported to be .999978c.

This does not make any sense. If you calculate Δt using C as the speed, then C should be the answer at the end, after you solve for velocity using the time dilation formula.

Shouldnt .999978c be reported as 3.0 E

^{8}m/s due to the significant figures?

The answer you get at the end just ends up being whatever value you assumed for "very high speeds."

Isn't this question impossible to answer unless you are given the actual velocity for the muon????

Thanks :-)

PS.

The next example in the book is the lengh contraction example for the muons reference frame. It uses 0.999978c as the velocity.