A novice golfer on the green takes three

Question

strokes to sink the ball. The successive dis-
placements are 7
.
7 m to the north, 1
.
9 m 45
◦
north of east, and 8
.
7 m 76
◦
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 dis-
placement?

Answer 1

Disp. = 7m[90o] + 9m[E45oN] + 7m[S76oW].

X = 9*Cos45 - 7*Cos76 = 1.84 m.
Y = 7 + 9*sin45 - 7*sin76 = 6.57 m.
Q1.

Tan A = Y/X = 6.57/1.84 = 3.57168.
A = 74.4o N. of E. = Direction.

Disp. = Y/sin A = 6.57/sin74.4 = 6.82 m

Answer 2

Disp. = 7m[90o] + 9m[E45oN] + 7m[W14oS]

X = 9*Cos45 + (-7*Cos14) = -0.428 m.
Y = 7 + 9*sin45 + (-7*sin14) = 11.7 m.
Q2.

Tan A = Y/X = 11.7/-0.428 = -27.26754.
A = -87.9o = 87.9o N. of W. = Direction.

Disp. = Y/sin A = 11.7/sin87.9 = 11.71 m