A golfer takes 3 putts to get the ball into the hole. The first putt displaces t

Question

A golfer takes 3 putts to get the ball into the hole. The first putt displaces the ball 3.66 meters north. The second putt moves the ball 1.83 meters east, and the third putt displaces the ball 0.91 south.

What is the magnitude and direction of the displacement needed to get the ball into the hole with a single putt?

Also, assume the golfer starts his putting location at x=0,y=0. What are the x (east-west) & y (north-south) coordinates of the hole?

Also, then convert to a vector, length and direction (angle).

Can you please show me all the work? Thanks so much!

Explanation / Answer

if we represent east is +x axis and north is +y axis so now vector representation

first putt = 3.66 j

second putt = 1.83 i

third putt = - 0.91 j

all displacements (Resultant) = 3.66 j + 1.83 i - 0.91 j = 1.83 i + 2.75 j

A)

magnitude = sqrt(1.83^2 + 2.75^2) = 3.3 m

direction = arctan(2.75/1.83) = 56.35 degrees counterclockwise from east

B)

x coordinate = 1.83 m or 1.83 m east

y coordinate = 2.75 m or 2.75 north

C)

Vector = 1.83 i + 2.75 j

length = sqrt(1.83^2 + 2.75^2) = 3.3 m

direction = arctan(2.75/1.83) = 56.35 degrees counterclockwise from +x axis

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