Respuesta :
Answer
given,
mean life time = 2.2 μs
distance above earth surface = 12.5 Km
speed = 3 x 10⁸ m/s
distance travel by the muons in his life time
distance = V t
= 3 x 10⁸ x 2.2 x 10⁻⁶
= 6.6 x 10² m
= 0.66 Km
mean life time of muson
[tex]t = \dfrac{\Delta t}{\sqrt{1-\dfrac{u^2}{c^2}}}[/tex]
[tex]t = \dfrac{2.2\times 10^{-6}}{\sqrt{1-\dfrac{(0.999 c)^2}{c^2}}}[/tex]
t = 4.92 x 10⁻⁵ s
A) The greatest distance a muon could travel during its lifetime is; 660 m
B) The mean lifetime of a muon as measured by an observer at rest on the earth is; 49.21 μs
In this question, we are required to find;
a) The greatest distance a muon could travel during its lifetime
b) At a speed of 0.999c, what is the mean lifetime of a muon as measured by an observer at rest on the earth? How far would the muon travel in this time?
We are given;
mean lifetime; t = 2.2 μs = 2.2 x 10⁻⁶ s
A) Since this is without relativity, then the greatest distance is gotten from the equation;
R = vt
where v is speed of light = 3 × 10⁸ m/s
Thus;
R = 3 × 10⁸ × 2.2 × 10⁻⁶
R = 660 m
B) We are told that the speed is now speed of 0.999c.
Thus, the factor by which the mean life is dilated is;
γ = 1/√(1 - 0.999²)
γ = 1/0.04471
γ = 22.37
Thus, the mean life is now;
22.37 × 2.2 × 10⁻⁶ = 49.21 × 10⁻⁶ s = 49.21 μs
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