ANSWER:
15.31 minutes
STEP-BY-STEP EXPLANATION:
Given:
Time (t) = 15 min
Speed (v) = 0.2 c
where c is the speed of light
We can determine the lifetime using the following formula:
[tex]\begin{gathered} \Delta t^{\prime}=\frac{\Delta t}{\sqrt{1-\frac{v^2}{c^2}}} \\ \\ \text{ We replacing:} \\ \\ \:\Delta t^{\prime}==\frac{15}{\sqrt{1-\frac{\left(0.2c\right)^2}{c^2}}} \\ \\ \Delta t^{\prime}=\frac{15}{\sqrt{1-0.4}} \\ \\ \Delta t^{\prime}=\frac{15}{\sqrt{0.96}} \\ \\ \Delta t^{\prime}=15.31\text{ min} \end{gathered}[/tex]Therefore, the lifetime of the neutron is 15.31 minutes.
