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.)
First, we solve for the x and y components of vectors A and B.
For vector A, the components are:
For vector B, the components are:
Since we know the components, we can now solve for the resultant vector R by adding the components together.
The resultant of the x-components is:
The resultant of the y-components is:
The magnitude of the resultant can be solved using the Pythagorean Theorem. That is:
The compass direction is
The compass direction is .