#### Find the following for path D in Figure 3.58:

#### (a) the total distance traveled and

#### (b) the magnitude and direction of the displacement from start to finish.

#### In this part of the problem, explicitly show how you follow the steps of the analytical method of vector addition.

**Solution:**

**Part A**

The total distance traveled following Path D is

**Part B**

Treat all motions upward and to the right positive, while downward and to the left negative.

The displacement in the x-direction is

The displacement in the y-direction is

The total displacement is

The direction angle from th x-axis is given by

Therefore, the displacement is 646.22 m, directed at 21.8 degrees north of east.