What Is the Expert Golfer's Ideal Single Stroke on the Green?

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The discussion focuses on calculating the ideal single stroke for an expert golfer on the green, given a novice's three strokes totaling specific displacements. The novice's movements include 4.00 m north, 2.00 m northeast (assumed to be at a 45-degree angle), and 1.00 m at 30 degrees west of south. Participants confirm that the resultant vector is derived by breaking down each displacement into its components and summing them. The angles for the second and third vectors are clarified, with northeast equating to 45 degrees and the third vector at 240 degrees. The final consensus is that adding the components will yield the expert golfer's optimal single displacement.
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A novice golfer on the green takes three strokes to sink the ball. The successive displacements are 4.00 m to the north, 2.00 m northeast, and 1.00 m at 30.0 degrees west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

I drew the picture, but am I to assume northeast means a 45 degree angle? The resultant vector is the sum of all three of these vectors. The first vector, broken down to its components, is 0i + 4j, or [0,4]. The second vector (if I'm assuming it has an angle of 45 degrees) has components of 2.00cos45 and 2.00 sin45, which makes 2/[sq.rt.]2 for both the x and y coordinates. And the third vector must be at an angle of 240 degrees, if it is just 30 degrees off of south in a western direction. Therefore, it is -120 or 240 degrees: h.c. = 1.00cos240 and v.c. = 1.00sin240. If these are all correct, I am just suppose to add each component to its respective component in order to get the resultant components of the expert golfer's shot, right?
 
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Yes, looks right to me. I agree, northeast seems to imply 45 degrees.
 
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