A golfer takes two putts to get the golf ball into hole once it is on the green.

Question

A golfer takes two putts to get the golf ball into hole once it is on the green. The first putt causes a displacement of 12 meters north. The second putt causes a displacement of 6 meters northwest. If we include the angles that each of these displacement vectors makes with the positive x axis, they can be written as: A = 12 meters at 90 degree B = 6 meters at 135 degree Add these two displacement vectors using components and determine the total displacement (A + B) of the golf ball from its starting position. Report the following information: the magnitude of the total displacement. the direction of the total displacement (with respect to the positive x axis).

Explanation / Answer

a)

here

displacement^2 = A^2 + B^2 - A * B * cos(theta)

d =sqrt( 12^2 + 6^2 - 6 * 12 * cos135 )

d = 16.78 m

b)

sin135 / 16.78 = sin(theta) / 6

theta = sin^-1( 0.252839)

theta = 14.65 deg

then

direction = 45 - 14.65 = 30.35 deg

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