Problem 84.

A body moves 4 km towards East from a fixed point A and reaches point B. Then it covers 5 km towards North and arrives at point C. Find the distance and directions of the net displacement.

Solution:

We show two displacements (travelled paths) in the figure.

The net (resultant) displacement is the vector sum of two displacements: the first displacement () and the second displacement ():

The easiest way to find the net displacement is to introduce coordinate system (axes x and y) and then find the x and y components of the net vector-displacement. The x and y components of the displacement () and displacement () are the following:

Then the x and y components of the net displacement is

Then the magnitude of the net displacement is

The direction of the net displacement is characterized by angle (shown in the figure), which can be found from the known x and y components of the net displacement: