The half-life observed by an observer at rest is 1.25 s
Explanation:
In this problem, the particle is travelling at a significant fraction of the speed of light: therefore, we have to consider the phenomenon of the time dilation. The half-life of the particle as measured by an observer at rest is given by
[tex]T=\frac{T_0}{\sqrt{1-(\frac{v}{c})^2}}[/tex]
where
[tex]T_0[/tex] is the proper half-life of the particle
v is the speed of the particle
c is the speed of light
For the particle in this problem,
[tex]T_0 = 1 s[/tex]
[tex]v=\frac{3}{5}c=0.6 c[/tex]
Substituting into the equation, we find:
[tex]T=\frac{1}{\sqrt{1-(\frac{0.6c}{c})^2}}=1.25 s[/tex]
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