### 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.