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 14PE:

Step 1 of 3:-

Here we need to find the distance and displacement of path D.

a)

Each block has sides of .

To get the distance we just simply add the lengths of the blocks for path D.

.

There are 13 blocks which come in the path, so we just added them. Distance is a scalar quantity and does not have a preferred direction, so we we able to do this.

So, the distance is .

b)

Step 2 of 3:-

Here we need to get the displacement which is a vector and it has a preferred direction and magnitude as well.

To get the displacement, we will join the starting and ending point.

Here the net displacement for path D is shown.

We can add the horizontal and vertical vectors to get the displacement vector.