Consider a cosmic ray colliding with a nucleus in the Earth's upper atmosphere that produces a muon which has velocity v = 0.916c. The muon then travels at constant velocity and lives 1.52 us as measured in the muon's frame of reference (You can imagine this as the muon's internal clock.) (a) How far (in km) does the muon in travel according to an Earth-bound observer? (b) How far (in km) does it travel as viewed by an observer moving with it? Base your calculation on its velocity relative to th Earth and the time it lives (proper time).

Consider a cosmic ray colliding with a nucleus in the Earth's upper atmosphere that produces a muon which has velocity v = 0.916c. The muon then travels at constant velocity and lives 1.52 us as measured in the muon's frame of reference (You can imagine this as the muon's internal clock.) (a) How far (in km) does the muon in travel according to an Earth-bound observer? (b) How far (in km) does it travel as viewed by an observer moving with it? Base your calculation on its velocity relative to th Earth and the time it lives (proper time).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

Consider a cosmic ray colliding with a nucleus in the Earth's upper atmosphere that produces a muon which has a
velocity v = 0.916c. The muon then travels at constant velocity and lives 1.52 µs as measured in the muon's frame of reference.
(You can imagine this as the muon's internal clock.)
(a) How far (in km) does the muon in travel according to an Earth-bound observer?
(b) How far (in km) does it travel as viewed by an observer moving with it? Base your calculation on its velocity relative to the
Earth and the time it lives (proper time).

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