Answer:
[tex]5.47399\times 10^{-8}\ s[/tex]
14.4513336 m
6.864 m
Explanation:
c = Speed of light = [tex]3\times 10^8\ m/s[/tex]
v = Velocity of object = [tex]2.6\times 10^{-8}\ m/s[/tex]
Time dilation is given by
[tex]\Delta t'=\dfrac{\Delta t}{\sqrt{1-\dfrac{v^2}{c^2}}}\\\Rightarrow \Delta t'=\dfrac{2.6\times 10^{-8}}{\sqrt{1-\dfrac{0.88^2c^2}{c^2}}}\\\Rightarrow \Delta t'=5.47399\times 10^{-8}\ s[/tex]
The mean lifetime as measured by an observer on Earth is [tex]5.47399\times 10^{-8}\ s[/tex]
For an observer on Earth the distance would be
[tex]d=0.88\times 3\times 10^8\times 5.47399\times 10^{-8}\\\Rightarrow d=14.4513336\ m[/tex]
The distance traveled is 14.4513336 m
Without time dilation
[tex]d=0.88\times 3\times 10^8\times 2.6\times 10^{-8}\\\Rightarrow d=6.864\ m[/tex]
The distance traveled would be 6.864 m
