(a) What would the observer in the laboratory measure for the particle\'s lifeti

Question

(a) What would the observer in the laboratory measure for the particle's lifetime?
_____ s

Imagine that there was a hypothetical observer traveling on the particle.
(b) What would the observer on the particle measure for the particle's lifetime?
_____ s
(c) What would the observer on the particle measure for the distance traveled?
_____ m

An unstable high - energy particle was created in the laboratory, and moved at a speed of 0.996c. Relative to a fixed location in the laboratory, the particle traveled a distance of 1.19 x 10^ - 3 m. (a) What would the observer in the laboratory measure for the particle's lifetime? _____ s Imagine that there was a hypothetical observer traveling on the particle. (b) What would the observer on the particle measure for the particle's lifetime? _____ s (c) What would the observer on the particle measure for the distance traveled? _____ m

Explanation / Answer

[a]

to= do/v= 1.19* 10-3 m/ 0.996c= 3.98*10-12s= 3.98ps [1ps[1picosecond]=10-12seconds]

[b]

t= t0 / [ 1-(v2/c2)] 1/2= 3.98*10-12/ [ 1- (0.9962c2/c2)] 1/2 =3.98*10-12 /0.089= 44.72*10-12s =44.72ps [time gets dilated]

[c]

d= d0*[ 1-(v2/c2)] 1/2=1.19* 10-3 m *[ 1- (0.9962c2/c2)] 1/2 = 1.19* 10-3* 0.089= 0.106* 10-3m = 0.106mm [length gets contracted from proper length d0]

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