A muon formed high in the Earth's atmosphere is measured by an observer on the Earth's surface to travel at speed v = 0.970c for a distance of 2.63 km before it decays into an electron, a neutrino, and an antineutrino

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A muon formed high in the Earth's atmosphere is measured by an observer on the Earth's surface to travel at speed v = 0.970c for a distance of 2.63 km before it decays into an electron, a neutrino, and an antineutrino 

(μ  e + v + v).
(a) For what time interval does the muon live as measured in its reference frame?
 µs

(b) How far does the Earth travel as measured in the frame of the muon?
 m
asked Apr 28, 2012 in Physics by Gummmys ~Expert~ (1,105 points)
    

1 Answer

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Best answer

 

Part A can be solved using the following formula:

Δt =  Δtp * squareroot( 1 -  (v/c)^2) (*where  Δt is observed time,  Δtp is proper time)

Δtp can be calculated as follows:

v = d/t    (*where v=velecity, d=distance, t=time)

therefore solving for t:

Δtp = d/v

After calculating Δtp, plug back into the first formula and solve for Δt.

 

Part B is solved with the following formula:

L = Lp * squareroot( 1 -  (v/c)^2)    (*where L=observed length, Lp=proper length)

Lp is simply the given distance, plug in the values into the formula and that is your answer.

 

answered Apr 28, 2012 by kirby ~Expert~ (3,020 points)
selected Apr 28, 2012 by Gummmys

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