Amuon is a type of unstable subatomic particle. when high-speed particles from outer space (sometimes called "cosmic rays") collide with atoms in the upper atmosphere, they can create muons which travel toward the earth. suppose a muon created in the atmosphere travels at a speed of 0.971c toward the earth's surface for a distance of 4.13 km, as measured by a stationary observer on earth, before decaying into other particles.
(a) as measured by the stationary observer on earth, how much time elapses (in s) between the muon's formation until its decay? 35.55 incorrect: your answer is incorrect. note that both the given speed of the muon and the given distance it travels is measured with respect to the earth. how is the time related to speed and distance? be sure to convert the speed to meters per second. s
(b) find the value of the gamma factor that corresponds to the muon's speed. 4.182 correct: your answer is correct.
(c) now imagine an observer that "rides along" with the traveling muon, moving at the same speed. from this observer's perspective, how much time elapses (in s) between the muon's formation until its decay? s
(d) again from the perspective of the observer traveling along with the muon, what distance (in m) does the muon travel, from its formation to its decay? m
(e) now imagine a third observer, who is traveling toward the muon at a speed of c 2 , as measured with respect to the earth. how does the muon's lifetime, as measured by this observer, compare to the lifetime as measured by the stationary observer on earth?
- the lifetime measured by the moving observer is the same as the lifetime measured by the observer on earth.
- the lifetime measured by the moving observer is shorter than the lifetime measured by the observer on earth.
- not enough information is known to make a comparison.
- the lifetime measured by the moving observer is longer than the lifetime measured by the observer on earth.