Question

You fly 4400 km across the United States on an airliner at 300 m/s . You return two days later traveling at the same speed. Have you aged more or less than your friends at home?By how much?

Answer 1

Answer:

$1.467\times 10^{-8}\ s$

Explanation:

Total Distance = $2\times 4400=8800\ km$

v = Speed = 300 m/s

c = Speed of light = $3\times 10^8\ m/s$

Time taken

$t=\dfrac{Distance}{Speed}\\\Rightarrow t=\dfrac{8800000}{300}\\\Rightarrow t=29333.33\ s$

Time dilation is given by

$t'=\dfrac{t}{\sqrt{1-\dfrac{v^2}{c^2}}}\\\Rightarrow t'=\dfrac{29333.33}{\sqrt{1-\dfrac{300^2}{(3\times 10^8)^2}}}$

The difference in time would be

$t'-t=\dfrac{29333.33}{\sqrt{1-\dfrac{300^2}{(3\times 10^8)^2}}}-29333.33=1.467\times 10^{-8}\ s$

My age will be less than my friends by $1.467\times 10^{-8}\ s$