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 +1.5 i^ - 3.0 j^, where the units are yards, i^ is to the right, and j^ is downfield. Subsequent displacements of the receiver are +7.5i^ (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^.

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.)

Express your answer using two significant figures.

Part B

In which direction must the quarterback throw the ball?

Express your answer using two significant figures.

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

At Enormous State University (ESU), the football team records itsplays using vector displacements, with the origin taken to be theposition of the ball before the play starts. In a certain passplay, the receiver starts at +1.5 -3.5 , where the units areyards, is to the right,and is downfield. Subsequentdisplacements of the receiver are +8.0 (in motion before the snap),+12 (breaksdownfield), (zigs), and (zags).Meanwhile, the quarterback has dropped straight back to aposition .

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

Express your answer using two significant figures.

B)In which direction must the quarterback throwthe ball?

Express your answer using two significant figures.

At Enormous StateUniversity (ESU), the football team records its plays using vectordisplacements, with the origin taken to be the position of the ballbefore the play starts. In a certain pass play, the receiver startsat +1.5 -3.5 , where the units areyards, is to the right,and is downfield. Subsequentdisplacements of the receiver are +8.0 (in motion before the snap),+12 (breaksdownfield), (zigs), and (zags).Meanwhile, the quarterback has dropped straight back to aposition .

{ReceiverAnd Quarterback Displacements}:
{Receiver} =
   = {+1.5, -3.5} + {+8.0, 0} + {0, +12} +{-6.0, +4.0} + {+12.0, +18.0} = {15.5, 30.5}
{Quarterback} = {0, 0} + {0, -7.0} = {0, -7.0}

A) How farmust the quarterback throw the ball? (Like the coach, you will bewell
advised to diagram the situation before solving it numerically.)Express your answer
using two significant figures.
{Quarterback Throw Displacement} = {15.5, 30.5} - {0,-7.0} = {15.5, 37.5}
{Quarterback Throw DISTANCE} = Sqrt[ (15.5)^2 +(37.5)^2] = 41 yards

B)In whichdirection must the quarterback throw the ball? Express your answerusing
two significant figures.

{Quarterback ThrowDisplacement} = {15.5,30.5} - {0, -7.0} = {15.5, 37.5}
{Quarterback Throw DIRECTION} =
        = 90 - ArcTan[ (37.5)/(15.5)]
     = 22 deg (right ofdownfield)