Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 7 - Applications of Trigonometry and Vectors - Summary Exercises on Applications of Trigonometry and Vectors - Page 339: 7c

Answer

The speed of the wind $u$ is 11.3 mph. The wind is blowing toward the northwest direction at a bearing of $315^{\circ}$.

Work Step by Step

$u = -8~i+8~j$ The speed of the wind is the magnitude of the vector $u$. We can find the magnitude of the vector $u$: $\vert u \vert = \sqrt{(-8)^2+8^2}$ $\vert u \vert = 11.3$ The wind is blowing toward the northwest. Since the horizontal component is equal in magnitude to the vertical component, the wind is blowing at a bearing of $270^{\circ}+45^{\circ} = 315^{\circ}$. The speed of the wind $u$ is 11.3 mph. The wind is blowing toward the northwest direction at a bearing of $315^{\circ}$.
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