Chapter 2, Problem 1CQ

A jogger runs due east along a straight jogging trail that is 2 km long. When she reaches the end of the path, she turns around and runs back to the west toward her initial starting point. In which direction does her displacement point after she has run a total distance of 3 km?

To determine

The direction in which the displacement of the jogger point after she run a total distance of $3\text{km}$.

Answer to Problem 1CQ

The displacement of the jogger point towards east after she run a total distance of $3\text{km}$

Explanation of Solution

Given that the jogger runs up to the end of the straight trail which is towards east and of distance $2\text{km}$ and runs back towards west such that she covers a distance of $3\text{km}$ in total. This implies that the distance she covered in the return run is $1\text{km}$ and the final position of the jogger is at the middle of the trail.

The displacement is the vector from the starting point of the journey to the end point. Hence, the displacement vector in this situation points from the initial position to the midpoint of the trail. That is, the displacement of the jogger point towards the east direction.