Answer to Question #136109 in Mechanics | Relativity for Naomi Johnson

Question

A football coach walks 10 meters eastward, then 18 meters westward, then 22 meter eastward, and finally 34 meters westward. What is the magnitude and direction of the displacement?

Answer 1

We will use the concept of vector to solve the problem.

Let $\hat i$ be the unit vector along east. Then, obviously, $-\hat i$ will be the unit vector along west.

In terms of these unit vectors the four displacements of the football coach are $10\hat i, -18\hat i, 22\hat i, \ and \ - 34 \hat i$ .

The resultant displacement = $10\hat i-18\hat i+22\hat i-34\hat i=-20\hat i$

Therefore, the magnitude of the displacement is 20 meters and $-\hat i$ indicates that the displacement is westward.

Answer: The magnitude of the displacement is 20 meters and direction is westward.