Murari walked 40 km towards North, took a left turn and walked 20 km. He again…

Concept

In direction problems, represent each movement as a displacement vector. Take east as the positive x-direction and north as the positive y-direction; west and south then have negative components.

Add horizontal components separately from vertical components. Opposite movements of equal length cancel, and the remaining vector gives both the distance and the direction from the starting point.

Application

1. Start at (0, 0). Moving 40 km north changes the position to (0, 40).

2. A left turn while facing north points west. Moving 20 km west changes the position to (-20, 40).

3. A second left turn while facing west points south. Moving 40 km south changes the position to (-20, 0).

Cross-check

• The 40 km northward and 40 km southward components cancel: 40 - 40 = 0.

• The only non-zero component is 20 km westward, so the displacement magnitude is 20 km and its direction is West.

Therefore, Murari is 20 km West of the starting point.