Question

A man walks 3 km north, then 4 km east, and finally 3 km south. How far is he from his starting point?

• A. 3 km
• B. 4 km
• C. 5 km
• D. 6 km

Hint:

Use coordinate geometry or vector addition for direction problems. Cancel opposite movements (e.g., north and south) to simplify.

Answer 1

The Correct Option is B

To determine the man's final distance from his origin, we must calculate his net displacement after a series of movements.

1. Core Principles:

- The man's journey comprises three segments: northbound, eastbound, and southbound.
- The objective is to ascertain the direct distance between his terminal location and initial position.
- This direct distance, or displacement, can be computed using the Pythagorean theorem within a Cartesian coordinate system.

2. Movement Analysis:

- Segment 1: 3 km north.
- Segment 2: 4 km east.
- Segment 3: 3 km south.

The man's starting point is designated as the origin (0,0).

3. Determining Final Coordinates:

- Following 3 km north: position is (0, 3).
- Subsequently moving 4 km east: position becomes (4, 3).
- Concluding with 3 km south: the final position is (4, 0), as the southbound movement cancels the northbound displacement.

4. Calculating Displacement:

Displacement is the linear distance connecting the origin (0, 0) to the terminal point (4, 0).

The distance formula yields:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = \sqrt{(4 - 0)^2 + (0 - 0)^2} = \sqrt{16} = 4 \text{ km} \]

Conclusion:

The man is located 4 km from his starting position.