THE mouns rain down more-or-less uniformly on the ground , althoughsome of them
ID: 1759197 • Letter: T
Question
THE mouns rain down more-or-less uniformly on the ground , althoughsome of them decay on the way since the moun is unstable with aproper half- life of about 1.5 x 10^-6 s. in a certianexperiements a moun detector is carried in a ballon to an altitudeof 2000 m, and in the course of 1 hour it registers 650 mounstraveling at 0.99c toward the earth. if an identical detectorremains at sea level, how many mouns would you expect it toregister in 1 hour?????This was essentially the method used in the first tests of timedilation, starting in the 1940's.
Explanation / Answer
gamma factor = = 1/(1-v^2/c^2) = 1/(1-.99^2) =7.09 in rest frame, half-life = 1.5*10^-6 s distance to sea-level = 2000/ = 282.1 m >>> due tolength contraction flight time to sea level = T = 282.1/(.99*3*10^8) = 9.5*10^-7 s The decay formula for is N = N0 e-(ln2 t/) so number expected at sea level is N = 650e-(ln2 T/) = 650e-(.693*.95/1.5)= 419 per hour. if we do the calculation in earth frame, half life = ' = (due to time dilation) =10.635*10^-6 s flight time = T' = 2000/.99c = 6.734*10^-6 s N = 650e-(ln2 T'/') =650e-(.693*6.734/10.635) = 419 per hour.
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