Recall, from this chapter, that the factor

Chapter 17, Problem 45TAS

(choose chapter or problem)

Recall from this chapter that the factor gamma \((\gamma)\) governs both time dilation and length contraction, where

               \(\gamma=\frac{1}{\sqrt{1-\left(\frac{v^{2}}{c^{2}}\right)}}\)

When you multiply the time in a moving frame by \(\gamma\), you get the longer (dilated) time in your fixed frame. When you divide the length in a moving frame by \(\gamma\), you get the shorter (contracted) length in your fixed frame.

Assume that rocket taxis of the future move about the solar system at half the speed of light. For a 1-hour trip as measured by a clock in the taxi, a driver is paid 10 stellars. The taxi-driver’s union demands that pay be based on Earth time instead of taxi time. If that demand is met, show that the new payment for the same trip would be 11.5 stellars.