A man walks 6 km to the East and then turns to the South and walks 5 km. Again he turns to the East and walks 6 km. Next, he turns to the North and walks 10 km. What is the shortest distance from his starting point to the final position?
Correct: A
Let the starting point be the origin (0,0).
1. Walks 6 km East: Position becomes (6, 0).
2. Turns South and walks 5 km: Position becomes (6, 0-5) = (6, -5).
3. Turns East and walks 6 km: Position becomes (6+6, -5) = (12, -5).
4. Turns North and walks 10 km: Position becomes (12, -5+10) = (12, 5).
The final position is (12, 5) relative to the starting point (0,0).
The horizontal displacement is 12 km East, and the vertical displacement is 5 km North.
The shortest distance is calculated using the Pythagorean theorem:
Distance = sqrt((12)^2 + (5)^2) = sqrt(144 + 25) = sqrt(169) = 13 km.