### (a) Repeat the problem two problems prior, but for the second leg you walk 20.0 m in a direction 40.0º north of east (which is equivalent to subtracting B from A —that is, to finding R′ =A−B ). (b) Repeat the problem two problems prior, but now you first walk 20.0 m in a direction 40.0º south of west and then 12.0 m in a direction 20.0º east of south (which is equivalent to subtracting A from B —that is, to finding R′′ = B – A = – R′ ). Show that this is the case.

**SOLUTION:**

**Part A**

We are required to solve for

The x-component of the resultant is:

The y-component of the resultant is:

The resultant is

The compass direction is

The compass direction is

**Part B**

The result is the same as that in Part A since the components did not change. Only the order has changed. This is consistent with the fact that