## Precalculus (6th Edition) Blitzer

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