A novice golfer on the green takes three strokes to sink the ball. The
successive displacements are 4.10 m to the north, 1.80 m northeast, and
0.90 m at 25.0° west of south. Starting at the same initial point, an
expert golfer could make the hole in what single displacement?

Solution:

Solve for the vertical and horizontal components of the vectors,

y = 4.1 + 1.8*SIN(45) - 0.9*COS(250)
y = 4.56 m

x = 1.8*COS(45) - 0.9*SIN(25)
x = 0.89 m

d = sqrt(4.56^2 + 0.89^2)
d = 4.64 m

angle = arctan(0.89/4.56)
angle = 11 degrees from vertical