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)
- If a map is placed in such a manner that east becomes southeast, then what will northeast become?
Point A is $30$ m to the North of point B. Point A is $10$ m to the west of point C. Point C is $20$m to the North of point D. Point E is $20$ m to the East of point D. Point F is $20$ m to the South of point E. What is the shortest distance from the point B to point E.
Rakesh left home and walked $5$km southwards, then turned right and walked $2$km and again turned right and walked $5$ km and finally again turned left and walked $5$ km. The shortest distance between the final position and home is.
- The door of Aman's house faces east. From the back side of his house, Aman walks straight 30m. Again he walks 20m after turning to his left, then he turns to his right and walks 30m. Finally he turn towards north and walks 20m and stops. So, what is the distance between the starting and the end point?
- Smitha runs 10 km south from her flat, turns left and walks 23 km again turns left and walks 40 km then turns right and walks 5 km to reach her office. In which direction is the office from her house?
