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 Question:
The question asks for the shortest distance (displacement) between the starting and ending points after a series of movements in cardinal directions. 
Step 2: Key Formula or Approach: 
We can solve this by calculating the net movement along the East-West axis and the North-South axis. Then, we use the Pythagorean theorem to find the straight-line distance. Let the starting point be the origin (0,0).
Distance = 
\( \sqrt{(\text{net horizontal displacement})^2 + (\text{net vertical displacement})^2} \) 
Step 3: Detailed Explanation: 
Let's break down Aman's movements: 
1. 1 km towards East: Net Eastward movement = +1 km. 
2. 5 km towards South: Net Southward movement = -5 km. 
3. 2 km towards East: Total Eastward movement = +1 km + 2 km = +3 km. 
4. 9 km towards North: Total North-South movement = -5 km (South) + 9 km (North) = +4 km (North). 
So, the final position relative to the starting point is: - 3 km to the East. - 4 km to the North. These two displacements form the two perpendicular sides of a right-angled triangle, with the hypotenuse being the direct distance from the start to the end point. Using the Pythagorean theorem: \[ \text{Distance}^2 = (\text{Eastward distance})^2 + (\text{Northward distance})^2 \] \[ \text{Distance}^2 = 3^2 + 4^2 \] \[ \text{Distance}^2 = 9 + 16 = 25 \] \[ \text{Distance} = \sqrt{25} = 5 \text{ km} \] 
Step 4: Final Answer: 
Aman is 5 km from his starting point.