Repeat the problem above, but reverse the order of the two legs of the walk; show that you get the same final result. That is, you first walk leg B , which is 20.0 m in a direction exactly 40º south of west, and then leg A , which is 12.0 m in a direction exactly 20º west of north. (This problem shows that A+B=B+A.)
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 .
No matter what is the order of the vectors we are adding, the result is still the same. This proves that .