Question

A person starts walking 5 km north, then turns right and walks 3 km. Then turns right again and walks 5 km. Finally, he turns left and walks 2 km. How far is he from the starting point?

• A. 5 km
• B. 3 km
• C. 2 km
• D. 4 km

Hint:

For direction problems, use a coordinate plane with the starting point as (0,0). Track each move as a vector (x,y) based on direction (North: +y, East: +x, etc.). Sum the x and y components to find the final position, then calculate the straight-line distance using the distance formula: $\sqrt{x^2 + y^2}$. Draw a diagram to visualize the path and check for consistency.

Answer 1

The Correct Option is A

To resolve this issue, we must systematically record the individual's movements and subsequently determine the direct distance between their initial and final locations.

1. Conceptual Framework:

- Cardinal Directions: North, East, South, West, with directional changes influencing orientation.
- Net Displacement: The shortest linear distance from the origin to the terminus.
- Application of Pythagorean Theorem: Employed for calculating distances within right-angled triangles formed by orthogonal movements.

2. Provided Movement Data:

- Proceed 5 km northward. - Execute a right turn (orienting eastward) and advance 3 km. - Execute another right turn (orienting southward) and advance 5 km. - Execute a left turn (orienting eastward) and advance 2 km.

3. Trajectory Analysis:

- Following the initial movement: 5 km north. - Following the second movement: 3 km east. - Following the third movement: 5 km south; this movement negates the initial 5 km north, resulting in a net zero north-south displacement relative to the starting point. - Following the fourth movement: 2 km east, aggregating the eastward displacement to a total of 3 km + 2 km = 5 km.

4. Displacement Calculation:

Net north-south displacement: 0 km (as the northward and southward movements are equal and opposite).
Net east-west displacement: 5 km eastward.
Final distance from origin: 5 km.

Conclusion:

The individual is located 5 km from their point of origin.