He again turns left and walks for 6 km.
At this point, he turns to his left and walks for 6 km. How far is he from his starting point? (All turns are 90-degree turns only, unless specified.)
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.
Important Questions from Direction and Distance (Notes)
- A woman leaves her home. She walks 40 m in North-West direction and then 90 m in South-East direction. Then, she moves 30 m in North direction. How far is she now from her initial position ?
- N sits to the North of L and West of M. L sits to the East of O. If everyone is facing North, which direction of O, is N?
I starts from Point A and drives 5 km towards the north. He then takes a right turn, drives 2 km, turns right and drives 9 km. He then takes a right turn and drives 7 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are $90^\circ$ turns only unless specified.)
A tourist drives $20 \text{ km}$ towards east, turns right and drives $6 \text{ km}$, then drives $6 \text{ km}$ towards west. He then turns to his left and drives $4 \text{ km}$ and finally turns right and drives $14 \text{ km}$. Where is he from his starting point?
- A Couple started to their offices in the morning from their home. While husband drives 3 km South and then 2 km to his right to reach his office, wife goes 2 km towards East for her office. With respect to husband's office, how far and in which direction is the wife's office ?
