Question

A quarterback takes the ball from the line of scrimmage, runs backward for 6 yards and then runs sideways parallel to the line of scrimmage for 8 yards. At this point, he throws a 46 yard forward pass straight down the field. What is the magnitude of the footballs resultant displacement?

Answer 1

Vector representation:

Let vector A be;

`\vec{A}=(-6\hat{i})\text{ yards}`

Vector B be;

`\vec{B}=(-8\hat{j})\text{ yards}`

Vector C be;

`\vec{C}=(46\hat{i})\text{ yards}`

The resultant displacement vector R is given as,

`\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}`

The magnitude of the resultant displacement vector is given as,

`\begin{gathered} \lvert\vec{R}\rvert=\sqrt[]{(40)^2+(-8)^2} \\ \approx40.79\text{ yards} \end{gathered}`

Therefore, the magnitude of the football's resultant displacement is 40.79 yards.