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

[cosmos42]

Homework Statement

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.

Homework Equations

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

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.)

 

[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?

 

[cosmos42]

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

What is meant by that statement?

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"