#### Suppose you first walk 12.0 m in a direction 20º west of north and then 20.0 m in a direction 40.0º south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements A and B , as in Figure 3.56, then this problem finds their sum R = A + B .)

## Solution:

Solve for the x and y components of the displacement.

The x-component of the displacement is:

The y-component of the displacement is:

The resultant displacement is therefore,

The compass direction is: