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: Understanding the Concept:
This problem involves tracking movement in different directions and calculating the final displacement from the starting point. We can visualize this on a coordinate plane.
Step 2: Key Formula or Approach:
Let the initial position be the origin (0, 0). We will track the net movement in the North-South and East-West directions.
Step 3: Detailed Explanation:
Let's trace the girl's path step-by-step:
1. Walks 20 meters towards North: The girl moves 20m up. Her position is now 20m North of the start.
2. Turning to her left, she walks 50 meters: From North, left is West. She moves 50m West. Her position is 20m North and 50m West of the start.
3. Turning to her right, she walks 40 metres: From West, right is North. She moves another 40m North. Her total northward distance from the start is now \(20 + 40 = 60\)m. Her position is 60m North and 50m West of the start.
4. Again, she turns to her right and walks 50 metres: From North, right is East. She moves 50m East. This eastward movement of 50m exactly cancels out her previous westward movement of 50m.
Final Position:
Her net movement East-West is \(50\text{m West} - 50\text{m East} = 0\text{m}\).
Her net movement North-South is \(20\text{m North} + 40\text{m North} = 60\text{m North}\).
So, her final position is 60 metres directly North of her initial position.
Step 4: Final Answer:
She is 60 metres from her initial position.