Q. 113 - Precalculus Enhanced with Graphing Utilities

Question

Keeping Up with the Sun How fast would you have to travel on the surface of Earth at the equator to keep up with the Sun (that is, so that the Sun would appear to remain in

the same position in the sky)?

Step-by-Step Solution

Answer

The speed that you should be moving on the surface of the earth is $1036.73$ mi/hr.

Step 1. Given Information

The problem asks how fast would a person travel on the surface of the earth at the equator to keep up with the speed of the sun.

To know what speed should you be travelling to match the speed of the Sun on the surface of the Earth, the formula for linear speed is needed$v=rw$

Step 2. Solving for linear speed

$$\begin{gathered} v=rw \\ v=\left(3960mi\right)\left(\frac{1 rev}{24 hr}\right) \\ v=\left(3960mi\right)\left(\frac{1 rev}{24 hr}\right)\left(\frac{2\mathrm{\pi } \mathrm{rad}}{1 rev}\right) \\ v=1036.73mile/hr \end{gathered}$$