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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?
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?