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Suman walks 8 km towards North, then turns left and walks 6 km, then turns right and walks 4 km, and finally turns right and walks 6 km. How far is she from the starting point?
12 km
14 km
10 km
18 km
12 km
Track net movement on X and Y axes: (North-South) = 8 + 4 = 12 km, (East-West) = 6 - 6 = 0 km; since the horizontal displacement cancels out, the distance is simply the sum of vertical movements.
Track net movement on X and Y axes: (North-South) = 8 + 4 = 12 km, (East-West) = 6 - 6 = 0 km; since the horizontal displacement cancels out, the distance is simply the sum of vertical movements.
Establish Coordinates
Starting at origin (0, 0): Walk 8 km North leads to (0, 8). Turn left (West) 6 km leads to (-6, 8). Turn right (North) 4 km leads to (-6, 12). Turn right (East) 6 km leads to (0, 12).
Calculate Final Displacement
The final position is (0, 12). The starting point is (0, 0). The distance between (0, 0) and (0, 12) is the square root of ((0-0)2 + (12-0)2), which equals 12 km.
B: 14 km is incorrect as it fails to account for the horizontal displacement canceling out; C: 10 km is incorrect as it assumes a diagonal hypotenuse calculation of 6 and 8, ignoring the additional 4 km walk; D: 18 km is incorrect as it simply adds all walk distances regardless of direction (8+6+4+6=24) or sub-components incorrectly.
A is correct because the final position is exactly 12 km North of the starting point, as the 6 km West and 6 km East movements cancel each other out.
In direction problems, always maintain separate running totals for North-South and East-West directions; opposite directions subtract, and same directions add.
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