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A man walks 6 km towards the North, then turns left and walks 8 km. He then turns right and walks 3 km. Finally, he turns right and walks 8 km. How far is he from the starting point?
9 km
12 km
14 km
17 km
9 km
Track net movement on X and Y axes using a coordinate system (North/South = Y, East/West = X). Net displacement = sqrt(x squared + y squared).
Track net movement on X and Y axes using a coordinate system (North/South = Y, East/West = X). Net displacement = sqrt(x squared + y squared).
Analyze coordinate displacements
Start at (0,0). Move North 6km (+6 Y); Move Left (West)тВИkm (-8 X); Move Right (North)тВГkm (+3 Y); Move Right (East)тВИkm (+8 X).
Calculate final position
Net X displacement = -8 + 8 = 0. Net Y displacement = 6 + 3 = 9. Final coordinate is (0, 9).
Calculate distance from origin
Distance = sqrt((0-0) squared + (9-0) squared) = sqrt(81) = 9 km.
B: 12 km is incorrect as it fails to account for the canceling of horizontal movements. C: 14 km is incorrect because it incorrectly sums distances without considering vector directions. D: 17 km is incorrect as it results from a simple arithmetic sum of all distances (6+8+3+8) which ignores movement cancellation.
A is correct because the net horizontal displacement is 0 km and the net vertical displacement is 9 km, placing the man exactly 9 km North of the starting point.
Always treat North/East as positive and South/West as negative when solving direction problems to avoid confusion with left/right turns.