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
where
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,
Substituting into the equation, we find:
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