Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 4 - Kinematics in Two Dimensions - Exercises and Problems - Page 106: 26

Answer

The plane's angular velocity with respect to the earth's surface is $7.96^{\circ}/h$

Work Step by Step

We can find $f$, the fraction of the earth's circumference that the plane flies. $f = \frac{5000~mi}{2\pi ~4000~mi}$ $f = 0.199$ We can find the angle in degrees that the plane flies with respect to the earth's surface. $\theta = (0.199)(360^{\circ})$ $\theta = 71.64^{\circ}$ We can find the plane's angular velocity with respect to the earth's surface. $\omega = \frac{\Delta \theta}{\Delta t}$ $\omega = \frac{71.64^{\circ}}{9.0~h}$ $\omega = 7.96^{\circ}/h$ The plane's angular velocity with respect to the earth's surface is $7.96^{\circ}/h$
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