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^ - 4.0 j^, where the units are yards, i^ is to the right, and j^ is downfield. Subsequent displacements of the receiver are +8.5 i^ (in motion before the snap), +10 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.)

b.) In which direction must the quarterback throw the ball?

Answer 1

starting position is

+ 1.0 i - 4.0 j

first displacement

+ 1.0 i - 4.0 j + 8.5 i

9.5 i - 4.0 j

then second displacement

9.5 i - 4.0 j + 10 j

9.5 i + 6 j

third displacement ( zigs)

9.5 i + 6 j - 6 i + 4 j

3.5 i + 10 j

fourth displacement ( zags)

3.5 i + 10 j + 12 i + 18 j

15.5 i + 28 j

the vector from the quarterback to the receiver is

15.5 i + 28 j - ( - 7j)

15.5 i + 35 j

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so,

How far must the quarterback throw the ball ?

d = sqrt ( 15.5² + 35²)

d = 38.278 yards

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In which direction must the quarterback throw the ball

angle = arctan ( 15.5 / 35)

angle = 23.88 degree