the football team at enormous state university (esu) uses vector displacements to record its plays, with the origin taken to be the position of the ball before the play starts. in a certain pass play, the receiver starts at 1.0i^−5.0j^, where the units are yards, i^ is to the right, and j^ is downfield. subsequent displacements of the receiver are 7.0i^ (he is in motion before the snap), 8.0j^ (breaks downfield), −7.0i^ 3.0j^ (zigs), and 11.0i^ 12.0j^ (zags). meanwhile, the quarterback has dropped straight back to a position −7.0j^.

We shall use the ideas connected to the vector sum to develop this issue. To achieve this, we will add the person's displacement vectors to determine the total distance he has gone from the initial point (0 position) to the destination position.

[tex]\overrightarrow R[/tex] = [tex](+1.0 \^{i} - 5\^{j}) + (7\^{i}) + (+12\^{j}) + (6.0\^{i} + 4.0\^{j}) + (+ 12.0\^{i} + 18.0\^{j})[/tex]

[tex]\overrightarrow R[/tex] = [tex]26\^{i} + 29\^{j}[/tex]

subtracting the quarterback's position [tex]\overrightarrow Q[/tex]

[tex]\overrightarrow Q[/tex] = [tex]-7.0\^{j}[/tex]

We can now get the relative location of the two individuals by subtracting the vectors; hence, the position between the individual and the quarterback is

[tex]\overrightarrow R[/tex] - [tex]\overrightarrow Q[/tex] = [tex]26\^{i} + 29\^{j}[/tex] - ([tex]-7.0\^{j}[/tex])

= [tex]26\^{i} + 36\^{j}[/tex]

The magnitude of the relative distance would be calculated using vector characteristics

[tex]|\overrightarrow R - \overrightarrow Q|[/tex] = [tex]\sqrt{26^2 + 36^2}[/tex]

[tex]|\overrightarrow R - \overrightarrow Q|[/tex] = 44.40 yards

The vector's direction would be determined by the tangent of the two vectors, which is

[tex]\theta = tan ^{-1} (\frac{36}{26} )[/tex] = 54.16°

As a result, with regard to 54.16 °, the quarterback will throw the ball 44.4 yards in one direction.

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Full question

At Enormous State University (ESU), the football team records its plays using vector displacements, with the origin taken to be the position of the ball before the play starts. In a certain pass play, the receiver starts at +1.0 i^ - 5.0 j^, where the units are yards, i^ is to the right, and j^ is downfield. Subsequent displacements of the receiver are +7.0 i^ (in motion before the snap), +12 j^ (breaks downfield), ?6.0i^+4.0j^ (zigs), and +12.0i^+18.0j^ (zags). Meanwhile, the quarterback has dropped straight back to a position ?7.0j^.

Part A

How far must the quarterback throw the ball? (Like the coach, you will be well advised to diagram the situation before solving it numerically.)

Part B

In which direction must the quarterback throw the ball?