Explanation:
It is given that,
The speed of light, c = 1000 mi/h
Distance, d = 2900 mi
Speed of the plane, v = 510 mi/h
(a) Let [tex]t_o[/tex] is the time elapsed according to your watch and t is the time elapsed according to a clock at the Los Angeles airport. It can be calculated using Einstein's theory of relativity as :
[tex]t=\dfrac{t_o}{\sqrt{1-\dfrac{v^2}{c^}}}[/tex]
[tex]t_o=t\sqrt{1-\dfrac{v^2}{c^}}[/tex].............(1)
[tex]t=\dfrac{d}{v}[/tex]
[tex]t=\dfrac{2900\ mi}{510\ mi/hr}[/tex]
t = 5.68 hrs
Equation (1) becomes :
[tex]t_o=5.68\sqrt{1-\dfrac{510^2}{1000}}[/tex]
[tex]t_o=4.88\ hrs[/tex]
(b) The time elapsed according to a clock at the Los Angeles airport is :
[tex]t=\dfrac{2900\ mi}{510\ mi/hr}[/tex]
t = 5.68 hrs
Hence, this is the required solution.
