Chapter 9.2, Problem 48PS

Solution

To state: The angle through which Earth has rotated during this time if the terminator moves across the planet’s surface as the planet rotates and it takes 4 hours for Earth’s terminator to move across the continental United States.

  

The resultant answer is ${60}^{\circ }\text{ or }\frac{\pi }{3}\text{ radian}$ .

Given information:

Earth’s terminator takes 4 hours to move across the continental United States.

Explanation:

It takes 24 hours to pass the whole turn of ${360}^{\circ }$ .

  $\begin{array}{c}24\text{ h}={360}^{\circ }\\ 1\text{ h}=\frac{{360}^{\circ }}{24}\\ 1\text{ h}={15}^{\circ }\end{array}$

The line moves through ${15}^{\circ }$ in 1 hour.

Now find movement of the line in 4 hours.

  $\begin{array}{c}4\times 1\text{ h}={15}^{\circ }\times 4\\ 4\text{ h}={60}^{\circ }\end{array}$

Therefore, in four hours the line moves through 60 degrees.

Now convert 60 degrees into radians, multiply the given angle measure by the conversion factor $\frac{\pi }{{180}^{\circ }}$ .

  ${60}^{\circ }\times \frac{\pi }{{180}^{\circ }}=\frac{\pi }{3}$

Therefore, in 4 hours, the line moves through $\frac{\pi }{3}$ radian.