Deals with the concepts that are important in this problem. a grasshopper makes four jumps. the displacement vectors are (1) 31.0 cm, due west; (2) 32.0 cm, 34.0 ° south of west; (3) 16.0 cm, 57.0 ° south of east; and (4) 16.0 cm, 75.0 ° north of east. find (a) the magnitude and (b) direction of the resultant displacement. express the direction as a positive angle with respect to due west.

(a) 46.6 cm

To calculate the total displacement, we need to resolve each vector along the x- and y- direction.

In the following, we take:

- East as positive x-direction, West as negative x-direction

- North as positive y-direction, South as negative y-direction

Vector A:

Vector B:

Vector C:

Vector D:

So the components of the total displacement are:

So the magnitude of the total displacement is:

(b) 19.8 degrees south of west

First of all, let's notice that:

- both components x and y of the total displacement are negative --> this means that the direction of the displacement is south of west

This means that the angle will be given by

where we have

Substituting, we find

and this angle is south of west.

answer: electrons