Calculating Muon Decay in Relativity: A Scientific Analysis

[student07]

Homework Statement

A muon has a lifetime of 2.20 x 10^-6 s when at rest, after which time it decays into other particles.
a) If the muon was moving at 0.99c, how far would it travel before decaying into other particles, according to Newtonian mechanics?
b) How long would the muon last, according to an observer in 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?

2. The attempt at a solution
a) 0.99c(3 x 10^8c) = 2.97 x 10^8
(2.97 x 10^8 m/s)(2.2 x 10^-6 s) = 653.4 m

b) Δtm = Δts/√(1-v^2/c^2)
Δtm = 2.2 x 10^-6 s / √(1-(0.99c)^2/c^2)
= 2.2 x 10^-6 s / √ (1 - 0.9801) = 1.56 x 10^-5 s

c) (2.97 x 10^8 m/s)(1.56 x 10^-5 s) = 4633.2 m

Not sure about c) any suggestions are appreciated thank you

 

[TSny]

Look good to me!

Is there something about part (c) that makes you unsure?

 

[student07]

Actually after giving it another look I got around it so thanks for your confirmation