Assignment 7: More on Vectors Item 7 Item 7 At Enormous State University (ESU),

Question

Assignment 7: More on Vectors Item 7 Item 7 At Enormous State University (ESU), the football Mod 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 +7.5 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 ls 7.0j

Explanation / Answer

given
reciever starts at r1 = i - 5 j, units in yards, i to the right, j downfield
subsequent displacements of reciever
s1 = 7.5i
s2 = 12 j
s3 = -6i + 4j
s4 = 12i + 18j

location of quarter b ack, R = -7 j

a. final location of reciever = r1 + s1 + s2 + s3 + s4 = i - 5j + 7.5i + 12j - 6i + 4j + 12i + 18j
   r = 14.5i + 29j
   but quarter back is at R = -7 j

   so distance between these two = sqroot(14.5^2 + (29 + 7)^2) = 38.810 yards
   so the quarter back has to throw the ball for 38.81 yards

b. direction = arctan((29+7)/14.5) = 68.08 deg CCW to the right

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