Vector representation:
Let vector A be;
[tex]\vec{A}=(-6\hat{i})\text{ yards}[/tex]Vector B be;
[tex]\vec{B}=(-8\hat{j})\text{ yards}[/tex]Vector C be;
[tex]\vec{C}=(46\hat{i})\text{ yards}[/tex]The resultant displacement vector R is given as,
[tex]\begin{gathered} \vec{R}=\vec{A}+\vec{B}+\vec{C} \\ =(-6\hat{i}-8\hat{j}+46\hat{i})\text{ yards} \\ =(40\hat{i}-8\hat{j})\text{ yards} \end{gathered}[/tex]The magnitude of the resultant displacement vector is given as,
[tex]\begin{gathered} \lvert\vec{R}\rvert=\sqrt[]{(40)^2+(-8)^2} \\ \approx40.79\text{ yards} \end{gathered}[/tex]Therefore, the magnitude of the football's resultant displacement is 40.79 yards.
