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 +2.0 i ^   - 4.0 j ^   , where the units are yards, i ^   is to the right, and j ^   is downfield. Subsequent displacements of the receiver are +9.0 i ^   (in motion before the snap), +11 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 ^   .

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.)

Express your answer using two significant figures.

b-

In which direction must the quarterback throw the ball?

Express your answer using two significant figures.

Answer 1

r1 = 2i - 4j

r2 = 9i + 11j

r3 = -6i + 4j

r4 = 12i + 18j

r5 = -7j

r = r1 + r2 + r3 + r4 + r5

r = 2i - 4j + 9i + 11j - 6i + 4j + 12i + 18j - 7j

r = 17i + 22j

r = sqrt(17^2+22^2)

r = 27.8 yards    <<<-----------answer

direction = tan^-1(22/17) = 52.3   degrees