A novice golfer on the green takes three

Question

strokes to sink the ball. The successive displacements are 3.6 m to the north, 2.8 m 45◦ north of east, and 2.2 m 59◦ west of south. Starting at the same initial point, an expert (lucky) golfer could make the hole in a single displacement.
What is the magnitude of this single displacement?

Answer 1

All angles are CCW from the +x-axis.

D = 3.6m[90o] + 2.8[45o] + 2.2[211o].

X = 3.6*Cos90 + 2.8*Cos45 + 2.2*cos211 =
0 + 1.98 - 1.89 = 0.09 m.

Y = 3.6*sin90 + 2.8*sin45 - 2.2*sin211 =
3.6 + 1.98 - 1.13 = 4.45 m.

D = Sqrt(X^2 + Y^2).