Question

Aman walks 1 km towards East and then he turns to South and walks 5 km. Again he turns to East and walks 2 km, after this he turns to North and walks 9 km. Now, how far is he from his starting point?

• A. 3 km
• B. 4 km
• C. 7 km
• D. 5 km

Hint:

For direction and distance problems, always calculate the net displacement for the North-South and East-West axes separately. The final distance is the hypotenuse of the right triangle formed by these net displacements.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a displacement problem based on the Pythagorean theorem. We track the net movement in the East-West (X-axis) and North-South (Y-axis) directions.
Step 2: Key Formula or Approach:
1. Let the starting point be \( (0,0) \).
2. Final Displacement \( = \sqrt{(\text{Net East/West distance})^2 + (\text{Net North/South distance})^2} \).
Step 3: Detailed Explanation:
Let's track Aman's coordinates step-by-step:
1. Walks 1 km East: Coordinates \( = (1, 0) \).
2. Turns South and walks 5 km: Coordinates \( = (1, -5) \).
3. Turns East and walks 2 km: Coordinates \( = (1 + 2, -5) = (3, -5) \).
4. Turns North and walks 9 km: Coordinates \( = (3, -5 + 9) = (3, 4) \).
Now, calculate the distance from the origin \( (0,0) \) to the final point \( (3,4) \):
\[ \text{Distance} = \sqrt{(3 - 0)^2 + (4 - 0)^2} \] \[ \text{Distance} = \sqrt{3^2 + 4^2} \] \[ \text{Distance} = \sqrt{9 + 16} \] \[ \text{Distance} = \sqrt{25} = 5 \text{ km} \]
Step 4: Final Answer:
Aman is 5 km away from his starting point.