Problem 40.

A boy walks to the store using the following path: 0.4 miles west, 0.2 miles north, 0.3 miles east.  What is his total displacement?  That is, what is the length and direction of the vector that points from her house directly to the store?

Solution:

The net displacement is the vector sum of three displacements as shown in the figure. It is more easier to find the net displacement in terms of components: x component (along east direction), y component (along north direction).

x component = x component of the first displacement + x component of the second displacement + x component of the third displacement = -0.4 + 0 + 0.3 = -0.1 miles.

y component = y component of the first displacement + y component of the second displacement + y component of the third displacement = 0 + 0.2 + 0 = 0.2 miles.

Then the magnitude of the net displacement is

The angle between the direction of the net displacement and west direction is

Then