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: 65


The values of the components of the vector are $22\sqrt{3}\text{i}+22\text{j}$.

Work Step by Step

The speed of the football $=44$ feet per second. The angle that the football makes with the horizontal $=30{}^\circ $. The vector component along the x-axis or horizontal is i and the vector component along they-axis or the vertical direction is j. Therefore, the equation becomes $\begin{align} & v=\left| \left| v \right| \right|\cos \theta \text{i}\,+\left| \left| v \right| \right|\sin \theta \text{j} \\ & =44\cos 30{}^\circ \text{i}+\,44\sin 30{}^\circ \text{j} \\ & =44\left( \frac{\sqrt{3}}{2} \right)\text{i}+44\left( \frac{1}{2} \right)\text{j} \\ & =22\sqrt{3}\text{i}\,+22\text{j} \end{align}$
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