Question

A muon formed high in the Earth's atmosphere is measured by an observer on the Earth's surface to travel at speed $v=$ $0.990 c$ for a distance of $4.60 \mathrm{km}$ before it decays into an electron, a neutrino, and an antineutrino $\left(\mu^{-} \rightarrow \mathrm{e}^{-}+\nu+\bar{\nu}\right)$ (a) For what time interval does the muon live as measured in its reference frame? (b) How far does the Earth travel as measured in the frame of the muon?

Name: Problem 6, Chapter 9: Principles of Physics a Calculus Based Text
Uploaded: 2020-07-13T18:42:48-08:00
Duration: 2 min 28 s
Channel: Rehmat Kazmi
Description: A muon formed high in the Earth's atmosphere is measured by an observer on the Earth's surface to travel at speed v= 0.990 c for a distance of 4.60 km before it decays into an electron, a neutrino, and an antineutrino (μ^- →e^-+ν+ν̅) (a) For what time interval does the muon live as measured in its reference frame? (b) How far does the Earth travel as measured in the frame of the muon?

   A muon formed high in the Earth's atmosphere is measured by an observer on the Earth's surface to travel at speed $v=$ $0.990 c$ for a distance of $4.60 \mathrm{km}$ before it decays into an electron, a neutrino, and an antineutrino $\left(\mu^{-} \rightarrow \mathrm{e}^{-}+\nu+\bar{\nu}\right)$ (a) For what time interval does the muon live as measured in its reference frame? (b) How far does the Earth travel as measured in the frame of the muon?

Principles of Physics a Calculus Based Text

Raymond A. Serway,… 5th Edition

Chapter 9, Problem 6

Instant Answer

Solved by Expert Rehmat Kazmi

07/13/2020

Step 1

This can be done using the formula for time dilation in special relativity, which is given by $\Delta t = \frac{\Delta t_0}{\sqrt{1 - \frac{v^2}{c^2}}}$, where $\Delta t_0$ is the proper time (time measured in the muon's reference frame), $v$ is the velocity of Show more…

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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 $v=$ $0.990 c$ for a distance of $4.60 \mathrm{km}$ before it decays into an electron, a neutrino, and an antineutrino $\left(\mu^{-} \rightarrow \mathrm{e}^{-}+\nu+\bar{\nu}\right)$ (a) For what time interval does the muon live as measured in its reference frame? (b) How far does the Earth travel as measured in the frame of the muon?