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Mayank starts from Point A and drives 18 km towards east. He then takes a right turn, drives 19 km, turns right and drives 21 km. He then takes a right turn and drives 25 km. He takes a final right turn, drives 3 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┬░ turns only unless specified.)
4 km to the south
5 km to the south
6 km to the south
8 km to the south
6 km to the south
Track net movement by resolving horizontal (E/W) and vertical (N/S) displacement. Since he moved 18E then 21E (total 39E) and returned 25W, he is 14E. WaitтАФcalculate simply: North/South balance reveals the final gap.
Track net movement by resolving horizontal (E/W) and vertical (N/S) displacement. Since he moved 18E then 21E (total 39E) and returned 25W, he is 14E. WaitтАФcalculate simply: North/South balance reveals the final gap.
Mapping the Path
Start at (0,0). Move 18E тЖТ (18,0). 19S тЖТ (18,-19). 21E тЖТ (39,-19). 25N тЖТ (39,6). 3E тЖТ (42,6). Wait, re-evaluating logic: Point A is (0,0). Final point P is (42,6).
Verifying Movement
Sum of Horizontal (E-W): 18 + 21 + 3 = 42 km East. Sum of Vertical (N-S): 19 South, 25 North. Net = 25N - 19S = 6 km North. Point P is 42 km East and 6 km North of A.
Return Direction
To reach Point A (0,0) from (42,6), one must travel 42 km West and 6 km South. The question specifically asks for the southward displacement required to align with the start latitude.
A: 4 km is incorrect; B: 5 km is incorrect; D: 8 km is incorrect based on the net North displacement of 6 km.
C is correct because the net vertical displacement from Point A is 6 km North, requiring a move of 6 km South to return to the original horizontal axis.
In displacement problems, always maintain separate running totals for North/South and East/West components to avoid mixing up axes.
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