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 solve the problem, we need to find the straight-line distance (displacement) of the man from his starting point after walking in different directions.

1. Understanding the Concepts:

- The man walks in three legs: north, east, and south.
- We want to find the shortest distance between his final position and the starting point.
- This shortest distance is the straight-line distance (displacement), which can be found using the Pythagorean theorem in a coordinate system.

2. Analyzing the Movement:

- First, he walks 3 km north.
- Then 4 km east.
- Finally, 3 km south.

Let’s consider his starting point as the origin (0,0).

3. Calculating the Final Position:

- After walking 3 km north, his position is (0, 3).
- After walking 4 km east, his position is (4, 3).
- After walking 3 km south, his position is (4, 0) because he moves back 3 km along the north-south axis.

4. Calculating the Displacement:

The displacement is the straight-line distance from the starting point (0, 0) to the final point (4, 0).

Using the distance formula:

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

Final Answer:

The man is 4 km away from his starting point.