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Sanjay starts from point Y and drives 32 km towards West. He then takes a left turn, drives 51 km, turns right and drives 66 km. He then takes a right turn and drives 14 km. He takes a right turn, drives 45 km. He then turns left, drives 37 km to stop at point Z. How far (shortest distance) and towards which direction should he drive in order to reach point Y again? (All turns are 90-degree turns only unless specified.)
51 km towards west
49 km towards east
53 km towards east
55 km towards north
53 km towards east
Track net movement by resolving horizontal (West/East) and vertical (North/South) displacements independently using a sign convention: West/South as negative and East/North as positive.
Track net movement by resolving horizontal (West/East) and vertical (North/South) displacements independently using a sign convention: West/South as negative and East/North as positive.
Calculate Net X-Coordinate (East-West)
Starting at Y(0,0): West 32 (-32), Right from North-facing is East +66, Right from East-facing is South, Right from South-facing is West, Right from West-facing is North. Wait: 32 West (-32), Left (facing South) 51, Right (facing West) 66, Right (facing North) 14, Right (facing East) 45, Left (facing North) 37. Sum: -32 (West) + 66 (East) + 45 (East) = +79 East total. Wait, let's re-verify: West 32 (-32), then South 51, then West 66 (-66), then North 14 (+14), then East 45 (+45), then North 37 (+37). Sum X: -32 - 66 + 45 = -53 (i.e., 53 km West). Sum Y: -51 + 14 + 37 = 0. Therefore, Z is 53 km West of Y.
Determine Displacement to reach Y
Since point Z is located at 53 km West relative to Y, to return to Y, one must travel 53 km in the opposite direction, which is East.
A: 51km West is incorrect as the Y-axis displacement is zero. B: 49km East does not match the net X-displacement of 53km. D: 55km North is incorrect as the net vertical displacement is zero.
C is correct because the net horizontal displacement of Sanjay from point Y to point Z is 53 km West, meaning he must travel 53 km East to return to point Y.
In direction problems, always maintain a running tally of X (East/West) and Y (North/South) coordinates to avoid confusion with complex sequences of turns.
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