Question

Suppose the speed of light were c= 1000 mi/h. You are traveling on a flight from Los Angeles to Boston, a distance of d=2900 mi. The plane's speed is a constant v=510 mi/h. (a) During the trip, how much time elapsed according to your watch? hours (b) During the trip, how much time elapsed according to a clock at the Los Angeles airport?

Answer 1

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 $t_o$ 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 :

$t=\dfrac{t_o}{\sqrt{1-\dfrac{v^2}{c^}}}$

$t_o=t\sqrt{1-\dfrac{v^2}{c^}}$.............(1)

$t=\dfrac{d}{v}$

$t=\dfrac{2900\ mi}{510\ mi/hr}$

t = 5.68 hrs

Equation (1) becomes :

$t_o=5.68\sqrt{1-\dfrac{510^2}{1000}}$

$t_o=4.88\ hrs$

(b) The time elapsed according to a clock at the Los Angeles airport is :

$t=\dfrac{2900\ mi}{510\ mi/hr}$

t = 5.68 hrs

Hence, this is the required solution.