VECTORS! physics help! please!?

Question

A person walks 100m E, then 280 m S, then he walks 150.0 m at a 30.0 S of W, and then 200.0 m and a 60.0 angle north of west. what is the person's resultant displacement measured from the starting point?

Answer 1

Let the starting point be the origin <0, 0> and East be the direction of the positive X axis.

The person first walks 100m East to point A. East is along th positive X axis, so the person's coordinates are now <100, 0>

The person then walks 280m South to point B. South is in the negative Y direction so the new coordinate are <100, 0> + <0, -280> or <100, -280>

The distance from point B to the starting point is therefore:

d = square root (100^2 + (-280)^2)

The person then walks 150m in a direction 30 degrees South of West to point C. That's an angle of 210 degrees, so the displacement for this step is 150

cos 210 = -sqrt(3)/2
sin 210 = -1/2

so this step = <-75sqrt(3), -75> and the location of C is
<100, -280> + <-75sqrt(3), -75> = <100 - 75sqrt(3), -355>

The rest is just more of the same.