Respuesta :
Answer: (a) t = 20.36.[tex]10^{-8}[/tex]s
(b) d = 60.225 m
Explanation: According to the Special Relativity Theory proposed by Albert Einstein, the laws of physics are the same for all non-accelerating observers and speed of light is the same in vaccum, no matter the speed the pbserver is travelling. with these statements, Einstein realized that space and time interwoven in a continuum called space-time, i.e., events that occur for one observer at the same time, occurs at different times for a second observer.
(a) To determine the lifetime and since the person is riding along:
t = [tex]\frac{t_{0} }{\sqrt{\frac{1-v^{2} }{c^{2} } } }[/tex] , in which:
t is time observed in the other time frame
t₀ is time in the observer's own reference
v is velocity of the object
c is the speed of light in vacuum (c=3.[tex]10^{8}[/tex]m/s)
Calculating:
t = [tex]\frac{3.4.10^{-8} }{\sqrt{\frac{1 - 0.986c^{2} }{c^{2} } } }[/tex]
t = [tex]\frac{3.4.10^{-8} }{\sqrt{0.028} }[/tex]
t = 20.36.[tex]10^{-8}[/tex]
The lifetime, according to the hypothetical person is 20.36.[tex]10^{-8}[/tex] seconds.
(b) The pion is moving at a speed of v = 0.986c. In 20.36 seconds,
the laboratory moves:
v=[tex]\frac{d}{t}[/tex]
d = v.t
d = 0.986.3.[tex]10^{8}[/tex].20.36.[tex]10^{-8}[/tex]
d = 60.225
The lab moved 60.225 meters.
