# Velocity of a muon if observed travel distance is 800 m?

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1. Feb 11, 2016

### cosmos42

1. The problem statement, all variables and given/known data
For a modern physics class, has to do with relativity
In a lab experiment a muon is observed to travel 800 m before disintegrating.
The mean lifetime of a muon is Tau = 2E-6 s
A muon's travel distance at the speed of light is x = tc = 0.66 km
Earth's atmosphere is x = 100 km
A student calculated the muon's speed to be faster than the speed of light, why is this wrong? Calculate the actual speed of the muon.

2. Relevant equations
Lorentz transformations
gamma = [1/(sqrt(1-(v^2/c^2)))]
t = x/c
Tau' = gamma(t)
velocity = distance/time

3. The attempt at a solution
Time moves slowly for particles moving at speeds close to that of light. This means that the lifetime of the muons is increased by t = t_earth/gamma. I will need to calculate the correct speed of the muon and compare it to that of photons. I can already conclude that nothing travels faster than the speed of light based on experimental evidence, and the muon has rest mass therefore it travels slower than the speed of light c. (Photons can travel at the speed of light therefore must have mass m=0.)

Last edited: Feb 11, 2016
2. Feb 11, 2016

### J Hann

"A muon's travel distance at the speed of light is x = tc = 0.66 km"W

What is meant by that statement?

3. Feb 11, 2016

### cosmos42

Great question, I have no idea. It was on one of my prof's lecture slides "Travel distance @ speed of light: x= t(0)c = 0.66 km" right underneath "Muon lifetime t(0) = 2.2E-6 s"