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A golfer, putting on a green, requires three strokes to "hole the ball." During the first putt, the ball rolls 4.6 m due east. For the second putt, the ball travels 2.5 m at an angle 20° north of east. The third putt is 0.50 m due north. What displacement (magnitude and direction relative to due east) would have been needed to "hole the ball" on the very first putt?

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Answer: To "hole the ball: on the very first putt is requered is required a 7.08 m displacement at an angle 11.03° north of east.

Explanation:

Let's add each stroke as vectors

  • Due east direction:  4.6 m + 2.5 cos(20°) m ≅ 6.95 m
  • Due north direction: 0.5 m + 2.5 sin(20°) m ≅ 1.35 m

So the total displacement is

[tex]\sqrt{6.95^2+1.35^2} \approx 7.08[/tex]

and the direction

[tex]\tan^{-1}\left({\frac{1.35}{6.95}}\right)\approx 11.03\deg[/tex]

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