Solving Rahul's Directional Movement Puzzle

This problem involves calculating the final distance from the starting point after a series of movements in different directions.

Step 1: Analyze Initial Northward Movement

Rahul starts by walking 6 km North. Let the starting point be O.

Position after Step 1: 6 km North of O.

Step 2: First Left Turn (Westward Movement)

Rahul turns left (90 degrees) and walks 3 km West.

Current Position: 6 km North and 3 km West of O.

Step 3: Second Left Turn (Southward Movement)

He turns left again (90 degrees) and walks 6 km South.

Analysis: The 6 km South movement cancels out the initial 6 km North movement. The net North-South displacement is now 0 km.

Current Position: 0 km North/South displacement (same latitude as O) and 3 km West of O.

Step 4: Third Left Turn (Eastward Movement)

He turns left one more time (90 degrees) and walks 6 km East.

Analysis: He was 3 km West of O. Walking 6 km East means he moves 3 km East to reach the North-South line passing through O, and then another 3 km East.

Net East-West Displacement: -3 km (West) + 6 km (East) = +3 km (East).

Step 5: Final Distance Calculation

The final position has zero North-South displacement and 3 km East displacement from the starting point O.

Therefore, the final distance from the starting point is the net Eastward displacement.

Distance = $\sqrt{(\text{Net East-West Displacement})^2 + (\text{Net North-South Displacement})^2}$

Distance = $\sqrt{(3 \text{ km})^2 + (0 \text{ km})^2}$

Distance = $\sqrt{9 \text{ km}^2}$

Distance = 3 km

Rahul is 3 km away from his starting point.