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

AI Thread Summary
The discussion centers on calculating the velocity of a muon that travels 800 meters before disintegrating, with a mean lifetime of 2 microseconds. A student mistakenly calculated the muon's speed as exceeding the speed of light, which is incorrect due to the principles of relativity. The correct approach involves using Lorentz transformations to account for time dilation, confirming that nothing with mass can exceed the speed of light. The muon's travel distance at light speed is noted as 0.66 km based on its lifetime, illustrating the relationship between time and distance in relativistic physics. The conversation highlights the importance of understanding these concepts in modern physics.
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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.)
 
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"A muon's travel distance at the speed of light is x = tc = 0.66 km"W

What is meant by that statement?
 
J Hann said:
"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"
 

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