Understanding the Walking Path Problem

This question involves calculating the final distance between a person's starting position and their ending position after following a specific path involving directions and distances.

Analyzing the Man's Movements

Let's break down the journey step by step:

• Step 1: Northward Journey The man starts at a point (let's call it A) and walks 12 km North. He reaches a new point (B). The distance AB = 12 km (North).
• Step 2: Eastward Journey From point B, he turns right (which is East, as he was facing North) and walks 8 km. He reaches point C. The distance BC = 8 km (East).
• Step 3: Southward Journey From point C, he turns right again (which is South, as he was facing East) and walks 12 km. He reaches his final point D. The distance CD = 12 km (South).

Calculating the Net Displacement

To find how far he is from the starting point (A), we need to determine his final position (D) relative to A. We can look at his displacement along the North-South axis and the East-West axis.

• North-South Displacement:
  • He moved 12 km North (positive direction).
  • He moved 12 km South (negative direction).
  • The net displacement along the North-South axis is $12 \text{ km} + (-12 \text{ km}) = 0 \text{ km}$.
• East-West Displacement:
  • He moved 8 km East (positive direction).
  • There was no movement West.
  • The net displacement along the East-West axis is $8 \text{ km}$.

Imagine plotting this on a graph. The 12 km North movement is cancelled out by the 12 km South movement. His final position D is therefore horizontally displaced from his starting point A.

Final Distance Calculation

Since the net displacement in the North-South direction is 0 km, the man ends up on the same horizontal line as his starting point. His final position D is entirely determined by his Eastward movement.

The distance from the starting point A to the final point D is equal to the net displacement in the East-West direction.

Distance from start = Net East-West Displacement = 8 km.

Conclusion

The man is 8 km away from his starting point.