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HarleyM
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Homework Statement
A muon has a lifetime of 2.2x10^-6 s when at rest, after which time it decays into other particles.
a)ignore any effects of relativity discussed in this lesson, if the muon was moving at 0.99c how far would it travel before decaying into other particles, according to Newtonian mechanics? *this line confuses me, I hope i obeyed them in my answer.. if anyone can let me know that would be great!
b) how long would the muon last according to an observer in the Earth's frame of reference who viewed the muon moving at 0.99c?
c) How far would the muon actually travel, when viewed moving at 0.99c?
d) Compare the distances travelled. Explain why this type of evidence is excellent support for the theory of relativity.
Homework Equations
Δtm = Δts/√(1-v2/c2)
The Attempt at a Solution
a) 0.99(3x10^8) = 2.97x10^8
2.97x10^8 m/s * 2.2x10-6 s = 653.4 m (not sure whether this is according to Newtonian mechanics?)
b) Δtm = Δts/√(1-v2/c2)
Δtm = 2.2x10-6/√(1-(0.99c)2/c2)
Δtm = 2.2x10-6/√(1-0.99)
Δtm = 2.2x10-5
c) 2.97x108 m/s * 2.2x10-5s
= 6534 m
D) this is excellent supportive evidence for the theory of relativity because it displays as matter approaches the speed of light significant time dilation occurs and the muon lasts much longer than it would with Earth as its reference frame.Does everything look logical ?
Thanks!