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Gautam starts from Point A and drives 30 km towards South. He then takes a left turn, drives 15 km, turns left and drives 42 km. He then takes a left turn and drives 7 km. He takes a final left turn, drives 12 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degree turns only unless otherwise specified.)
5 km towards West
8 km towards West
10 km towards West
10 km towards East
8 km towards West
Track the net vertical (North/South) and horizontal (East/West) displacements separately to find the final vector relative to the starting point.
Track the net vertical (North/South) and horizontal (East/West) displacements separately to find the final vector relative to the starting point.
Coordinate Mapping
Start at (0,0). Move 30 km South: (0, -30). Left turn (East) 15 km: (15, -30). Left turn (North) 42 km: (15, 12). Left turn (West) 7 km: (8, 12). Left turn (South) 12 km: (8, 0).
Final Displacement Calculation
Point P is at (8, 0), where A is (0, 0). To reach A from (8, 0), one must travel 8 km West. Reviewing the prompt options, 8 km West is the required correction.
A: 5 km West is incorrect as the net displacement is 8 km. C: 10 km West is incorrect. D: 10 km East moves further away from the origin (0,0).
B is correct because the cumulative net displacement from the origin A to Point P is 8 km East, meaning Gautam must travel 8 km West to return to point A.
In direction problems, always maintain a simple Cartesian coordinate system (x,y) to avoid confusing left/right turns under fatigue.
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