Answer
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
$\begin{align}
& v=\left| \left| v \right| \right|\cos \theta \text{i}\,+\left| \left| v \right| \right|\sin \theta \text{j} \\
& =30\cos 45\text{i}\,+30\sin 45\text{j} \\
& =30\left( \frac{\sqrt{2}}{2} \right)\text{i}\,+30\left( \frac{\sqrt{2}}{2} \right)\text{j} \\
& =15\sqrt{2}\text{i}\,+15\sqrt{2}\text{j}
\end{align}$
