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

Step-by-step 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=\frac{t_o}{\sqrt{1-(v^2)/(c^)}}`

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

`t=(d)/(v)`

`t=(2900\ mi)/(510\ mi/hr)`

t = 5.68 hrs

Equation (1) becomes :

`t_o=5.68\sqrt{1-(510^2)/(1000)}`

`t_o=4.88\ hrs`

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

`t=(2900\ mi)/(510\ mi/hr)`

t = 5.68 hrs

Hence, this is the required solution.