Question

A girl walks 20 meters towards North. Then, turning to her left, she walks 50 meters. Then, turning to her right, she walks 40 metres. Again, she turns to her right and walks 50 metres. How far is she from her initial position?

• A. 60 metres
• B. 50 metres
• C. 20 metres
• D. 40 metres

Hint:

In direction-based problems, keep track of the net movement along two perpendicular axes (e.g., North-South and East-West). Opposite movements cancel each other out, simplifying the calculation of the final distance.

Answer 1

The Correct Option is A

Step 1: Concept Overview:
This problem requires calculating the final displacement by tracking movement in cardinal directions, visualized on a coordinate plane.
Step 2: Methodology:
Assume the starting point as the origin (0, 0). We will sum movements along the North-South axis and the East-West axis independently.
Step 3: Detailed Walkthrough:
Tracing the path:
1. 20 meters North: Position is 20m North of start.
2. Turns left, walks 50 meters: Left from North is West. Position is 20m North, 50m West of start.
3. Turns right, walks 40 meters: Right from West is North. Total Northward movement is \(20 + 40 = 60\)m. Position is 60m North, 50m West of start.
4. Turns right, walks 50 meters: Right from North is East. This 50m East movement cancels the 50m West movement.
Resulting Position:
Net East-West displacement: \(50\text{m West} - 50\text{m East} = 0\text{m}\).
Net North-South displacement: \(20\text{m North} + 40\text{m North} = 60\text{m North}\).
The final location is 60 meters directly North of the starting point.
Step 4: Conclusion:
The final distance from the initial position is 60 metres.