Directional Movement Analysis
Lokesh's movements can be tracked step-by-step:
- Starts at a point (let's call it Origin).
- Runs 4 km East.
- Takes a 90° left turn, now facing North. Runs 3 km North.
- Takes another 90° left turn, now facing West. Runs 4 km West.
Final Direction Determination
After the final 90° left turn, Lokesh runs 4 km West. Therefore, his final facing direction is West.
Shortest Distance Calculation
Let's map the movements:
- Eastward movement: 4 km
- Northward movement: 3 km
- Westward movement: 4 km
The 4 km Eastward movement and the 4 km Westward movement cancel each other out in the East-West dimension. The only remaining displacement from the starting point is the 3 km Northward movement.
The path forms a rectangle where Lokesh starts at one corner, moves along two sides (East and North), and then moves parallel to the starting East-West line but 3 km North of it. His final position is directly 3 km North of the starting point.
The shortest distance back to the starting point is the straight-line distance, which is equal to the net Northward displacement.
Shortest Distance = $\sqrt{(\text{Net East-West displacement})^2 + (\text{Net North-South displacement})^2}$
Net East-West displacement = 4 km (East) - 4 km (West) = 0 km
Net North-South displacement = 3 km (North)
Shortest Distance = $\sqrt{(0 \text{ km})^2 + (3 \text{ km})^2} = \sqrt{0 + 9} = \sqrt{9} = 3$ km.
Thus, Lokesh is facing West and the shortest distance to reach back the starting point is 3 km.
Similar Questions
- Mahesh was facing east when he started from home. He took two right turns and one left turn to reach his school. In which direction, is he facing after reaching his school?
- Muneer ran 340 steps towards north and then ran 90 steps after turning to his left. He then ran 130 steps towards his right. He then, turned towards his right and ran 90 steps. From there, he turned towards his right and ran another 240 steps. How far and in which direction is Muneer with respect to the starting point?
- Rohit walked towards the West and took a turn at $45^\circ$ in the clockwise direction. He again turned at $180^\circ$ in the clockwise direction. Lastly, he turned $270^\circ$ in the anti-clockwise direction. In which direction was Rohit facing at last?
Ali drives 12 km to the west from point P. He then takes a right turn, drives 6 km and reaches point Q. From there, he takes a right turn, drives 5 km and reaches point S. He then takes a final right turn, drives 10 km and stops at point T.
Which of the following will take him to point P from point T?
- Ravish Kumar starts running facing towards the south. He runs for 20 m, then takes a left turn, and then runs for another 30 m. Again, he takes a left turn and runs 70 m. He then finally turns left and walks 30 m.
What is the current position of Ravish with respect to the starting point? (All turns are $90^\circ$ turns only) - Deepika starts her evening walk facing north and walks for 2 km. Then, she takes a right turn and walks for another 2 km. Finally, she takes a left turn and walks for another 3 km. Which direction is she facing now? (All turns are 90° turns only)
Mr. Yorly starts from Point A and drives 6 km towards South. He then takes a right turn, drives 37 km, turns right and drives 42 km. He then takes a right turn and drives 47 km. He takes a final right turn, drives 36 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 degrees turns only unless specified.)
Akshay starts from Point A and drives 12 km towards the north. He then takes a right turn, drives 15 km, turns right and drives 17 km. He then takes a right turn and drives 18 km. He takes a final right turn, drives 5 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-degree turns only unless specified.)
Sikar starts from Point A and drives 17 km towards the north. He then takes a left turn, drives 14 km, turns left and drives 18 km. He then takes a left turn and drives 19 km. He takes a final left turn, drives 1 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-degree turns only unless specified.)
Mr. Yorly starts from Point A and drives 17 km towards East. He then takes a left turn, drives 18 km, turns left and drives 30 km. He then takes a left turn and drives 31 km. He then takes a left turn, drives 9 km, turns left and drives 6 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 degrees turns only unless specified.)
Important Questions from Direction and Distance Turns
Shweta starts walking from her office and walks 150 m towards the south, then she turns right and walks 80 m, and then she turns left and walks 60 m. She finally turns left and walks 280 m to reach a bank. What is the shortest distance between her office and the bank?
Starting from her home, a woman walks 10 km towards the west. She turns left and walks 25 km. Again she turns left and walks 10 km. After that, she again turns left and walks 5 km. How far is she from her house now?
A. 35
B. 20
C. 25
D. 40
A man travels 15 km towards the east, then turns right and travels 20 km. He then turns left and travels 30 km. Finally, he takes a right turn and covers 40 km. The shortest distance between the starting point and the destination is:
A man starts from point ‘O’, travels 20 km towards East to reach point ‘A’, turns right and travels 10 km to reach point 'B', turns right and travels 9 km to reach point 'C', turns right and travels 5 km to reach point 'D', turns left and travels 12 km to reach point 'E' and then turns right and travels 6 km to reach point 'F'.
In which direction is the man facing now?
Lalit walks 9 km east, turns left and walks another 8 km. He again takes a left and walks another 3 km. How far and in which direction is he now from his starting point?
