Calculate DILATED LIFETIME of muon traveling close to speed of light

AI Thread Summary
To calculate the dilated lifetime of a muon traveling at 2.995 x 10^8 m/s, the proper lifetime of 1.500 x 10^-6 seconds is used in the formula delta t = delta t0 / [sqrt(1 - (v^2/c^2))]. Substituting the values, the calculation yields a dilated lifetime of approximately 2.599 x 10^-5 seconds. The answer should be rounded to three significant figures, resulting in 2.60 x 10^-5 seconds. This approach confirms the correct application of relativistic time dilation principles.
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Homework Statement



A muon is traveling with a speed of v = 2.995x10^8 m/s. Calculate the value of the dilated lifetime for this muon. Assume that the speed of light is c = 3.000 x 108 m/s and that the proper lifetime of the muon is 1.500 x 10-6 s.

Note: Do your calculations to 4 significant figures. Then round off to give an answer good to 3 significant figures. Be sure to include the correct abbreviation for the SI unit.


Homework Equations



Dilated lifetime
delta t = delta t0 / [sqrt 1 - (v2/c2)]


The Attempt at a Solution



How do I incorparoate the proper lifetime of the muon (1.500x10-6sec)?
 
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I replaced the numerator Delta t0 with the proper lifetime.

My answer is 2.599 x 10-5 seconds.

Is this correct??
 

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