Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.6 - Vectors - Exercise Set - Page 782: 66


The value of the components of the vector is $15\sqrt{2}i+15\sqrt{2}j$.

Work Step by Step

The magnitude of the force $=30$ pounds. The angle that the football makes with the horizontal $=45{}^\circ $. The vector component along the x-axis or horizontal is i and the vector component along the y-axis or the vertical direction is j. Therefore, the equation becomes $\begin{align} & v=\left| \left| v \right| \right|\cos \theta \text{i}\,+\left| \left| v \right| \right|\sin \theta \text{j} \\ & =30\cos 45\text{i}\,+30\sin 45\text{j} \\ & =30\left( \frac{\sqrt{2}}{2} \right)\text{i}\,+30\left( \frac{\sqrt{2}}{2} \right)\text{j} \\ & =15\sqrt{2}\text{i}\,+15\sqrt{2}\text{j} \end{align}$
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