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Amit starts from Point A and drives 35 km towards East. He then takes a right turn, drives 17 km, turns right and drives 15 km. He then takes a left turn and drives 13 km. He takes a final right turn, drives 20 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.)
28 km towards South
30 km towards East
30 km towards North
28 km towards North
30 km towards North
Track net displacement on X and Y axes independently. Amit's total horizontal shift and vertical shift from A determine the return vector.
Track net displacement on X and Y axes independently. Amit's total horizontal shift and vertical shift from A determine the return vector.
Coordinate Mapping
Starting at (0,0): 1) East 35km (+35, 0). 2) Right turn (South)тВБтВЗkm (+35, -17). 3) Right turn (West)тВБтВЕkm (+20, -17). 4) Left turn (South)тВБтВГkm (+20, -30). 5) Right turn (West)тВВтВАkm (0, -30). Current position P is (0, -30). Wait, re-evaluating: Start (0,0) тЖТ (35,0) тЖТ (35, -17) тЖТ (20, -17) тЖТ (20, -30) тЖТ (0, -30). Final pos relative to A is 0 East, 30 South. Re-reading: Point P is reached by: 35E, 17S, 15W, 13S, 20W. Total X: 35-15-20 = 0. Total Y: -17-13 = -30. Thus P is 30 km South of A.
Verify Directions
To return from (0, -30) to (0,0), one must travel 30 km North. Looking at provided options, '30 km towards North' is the correct match.
A: 28 km South is incorrect magnitude/direction. B: 30 km East is incorrect direction. D: 28 km North is incorrect magnitude.
C is correct because the net displacement of the path brings Amit to a point 30 km South of Point A, requiring a 30 km North movement to return.
Always convert directional turns into +/- X and Y coordinate changes to avoid confusion in complex multi-turn problems.
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