A jet plane travels around the world at 2 000 mi/hr (894 m/s). Two accurate atomic clocks measure the times of flight, one on board the plane and the second on Earth. If it takes 12 hours to complete the journey, what will the time difference (in μs) be?
A) 0.75
B) 0.50
C) 0.25
D) 1.0
E) 0.19

Question

Quizplus · Accepted Answer

The time difference is due to the time dilation effect of special relativity. The formula for time dilation is:$$t' = t/\gamma$$where:* t' is the time measured in the moving frame (the plane)* t is the time measured in the stationary frame (the Earth)* γ is the Lorentz factor, which is given by:$$\gamma = 1/\sqrt{1 - v^2/c^2}$$where:* v is the velocity of the moving object* c is the speed of lightIn this case, the velocity of the plane is 894 m/s and the speed of light is 299,792,458 m/s. Plugging these values into the equation for γ, we get:$$\gamma = 1/\sqrt{1 - (894 m/s)^2/(299,792,458 m/s)^2} = 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

A Jet Plane Travels Around the World at 2 000