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A golfer takes three strokes to get the ball into the hole once he is on the green. The first stroke displaces the ball 12 ft. north, the second stroke 6.0 ft. southeast, and the third stroke 3.0 ft. southwest. What displacement was needed to get the ball into the hole on the first stroke?

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  1. displacement
    = (0,12) + 6(cos45°, -sin45°) + 3(-cos45°, -sin45°)
    = (0,12) + (6/√2, -6/√2) + (-3/√2, -3/√2)
    = (3/√2 , (12√2-9)/√2 )
    = appr (2.12 , 5.64)

    magnitude = 6.02
    angle with x-axis:
    tan Ø = 5.64/2.12
    Ø ≐ 69.4°

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