Answer:
[tex]4.82383\times 10^{-6}\ s[/tex]
1316.90559 m
Explanation:
[tex]\Delta T'[/tex] = Time measured in the laboratory
[tex]\Delta T[/tex] = Time measured in its own frame of reference = [tex]2.2\times 10^{-6}\ s[/tex]
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
v = 0.91 c
Time dilation is given by
[tex]\Delta T'=\dfrac{\Delta T}{\sqrt{1-\dfrac{v^2}{c^2}}}\\\Rightarrow \Delta T'=\dfrac{2\times 10^{-6}}{\sqrt{1-\dfrac{0.910^2c^2}{c^2}}}\\\Rightarrow \Delta T'=4.82383\times 10^{-6}\ s[/tex]
The average lifetime is measured in the laboratory is [tex]4.82383\times 10^{-6}\ s[/tex]
Distance measured would be
[tex]L=v\Delta T'\\\Rightarrow L=0.91\times 3\times 10^8\times 4.82383\times 10^{-6}\\\Rightarrow L=1316.90559\ m[/tex]
The distance is 1316.90559 m
