University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 1 - Units, Physical Quantities, and Vectors - Problems - Exercises - Page 29: 1.40

Answer

(a) $117^{\circ}$ with the x-axis. (b) $15.9^{\circ}$ (c) $63.4^{\circ}$

Work Step by Step

Throughout, we use the general fact that the angle a vector makes with the x-axis, $\theta$, can be related to its components $A_x$ and $A_y$ as $tan \theta = \frac{A_y}{A_x}$. Evaluating this ratio for each of the three vectors, we get . . . for (a): the required angle = $arctan(\frac{-6}{3}) = 117^{\circ}$ for (b): the required angle = $arctan(\frac{2}{7}) = 15.9^{\circ}$ for (c): the required angle = $arctan(\frac{8}{4}) = 63.4^{\circ}$
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