Vector Displacement [closed]

Question

A novice golfer on the green takes three strokes to sink the ball. The successive displacements are 4.10 m to the north, 1.90 m northeast, and 1.00 m at 25.0° west of south. Starting at the same initial point, an expert golfer could make the hole in what single displacement?

___ m

____ north of east

I'm stuck on this problem and don't know how I would go about solving this problem. Could someone explain how to solve it with steps for me, I'm mostly interested in understanding how to do this rather than just getting the answer.

Answer 1

(1) express each displacement as a two-component xy vector where x is east and y is north*.

(2) find the resultant vector by adding the three vectors together. This is done by adding all of the x components together and then all of the y components together.

(3) convert the resultant vector to polar coordinates to find the distance and angle.

*For example, the 3rd displacement vector is 1.00 m long and has an angle of -115 degrees (south is -90 degrees). The x and y components are:

$x_3 = 1.00m \cdot \cos(-115^\circ) = -0.4226m$

$y_3 = 1.00m \cdot \sin(-115^\circ) = -0.9063m$