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A person walks 5 km towards the North, then turns right and walks 4 km. He then turns left and walks 3 km. Finally, he turns left and walks 4 km. How far is he from the starting point?
8 km
9 km
7 km
10 km
8 km
Track net movement by separating North-South and East-West vectors: North/South = 5 + 3 = 8 km, East/West = 4 - 4 = 0 km.
Track net movement by separating North-South and East-West vectors: North/South = 5 + 3 = 8 km, East/West = 4 - 4 = 0 km.
Coordinate Mapping
Assume starting point (0,0). Move 5 km North: (0, 5). Turn right (East)тВД km: (4, 5). Turn left (North)тВГ km: (4, 8). Turn left (West)тВД km: (0, 8).
Final Displacement Calculation
The person ends at position (0, 8). The distance from (0, 0) to (0, 8) is calculated as the square root of (0-0)2 + (8-0)2, which equals 8 km.
B: 9 km is incorrect as the vertical total is 8 and horizontal displacement is 0. C: 7 km is incorrect as it fails to sum the vertical steps (5+3). D: 10 km is incorrect as it miscalculates the net displacement geometry.
A is correct because the person moves a total of 8 km North and ends up directly North of the starting point with 0 km East-West deviation.
Always resolve moves into X and Y axis components; turns are simply +/- operations on the relevant coordinate axis.