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Rohan starts from Point M and walks 10 km towards the East. He turns left and walks 8 km, then turns right and walks 5 km. He turns right again and walks 8 km. Finally, he turns left and walks 3 km to reach Point N. How far (shortest distance) is he from the starting point?
18 km
15 km
12 km
20 km
18 km
Track net movement by separating East-West and North-South displacements. Total Horizontal = 10 + 5 + 3 = 18 km East; Total Vertical = 8 (North) - 8 (South) = 0 km.
Track net movement by separating East-West and North-South displacements. Total Horizontal = 10 + 5 + 3 = 18 km East; Total Vertical = 8 (North) - 8 (South) = 0 km.
Calculate horizontal net displacement
Rohan moves 10 km East, then 5 km East (after right turn), then 3 km East (after left turn). Total East displacement = 10 + 5 + 3 = 18 km.
Calculate vertical net displacement
Rohan moves 8 km North (after left turn), then 8 km South (after second right turn). Net vertical displacement = 8 - 8 = 0 km.
Final displacement calculation
Using the Cartesian coordinate system, the final position is (18, 0). The shortest distance from origin (0, 0) is the square root of (18 squared + 0 squared) = 18 km.
B: 15 km is incorrect as it ignores the final 3 km movement. C: 12 km is incorrect as it fails to sum the total horizontal distance. D: 20 km is incorrect as it incorrectly adds the vertical components instead of cancelling them.
A is correct because the final position of Rohan is 18 km directly East of his starting point M.
In direction problems involving multiple turns, always resolve North/South and East/West components separately to avoid unnecessary complex geometry calculations.