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(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.