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Keval starts from point Y and drives 77 km towards North. He then takes a right turn, drives 34 km, turns right and drives 36 km. He then takes a right turn and drives 65 km. He then turns left, drives 41 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.)
31 km towards east
29 km towards west
30 km towards east
33 km towards north
31 km towards east
Track the net North-South (Y) and East-West (X) displacements separately using the start point as (0,0) and use Pythagoras or direct coordinate differences to find the distance and direction to return.
Track the net North-South (Y) and East-West (X) displacements separately using the start point as (0,0) and use Pythagoras or direct coordinate differences to find the distance and direction to return.
Calculate Net Vertical Displacement (North-South)
Starting at Y(0,0): Move North 77km (+77), then Right (East) 34km, then Right (South) 36km (-36), then Right (West) 65km, then Left (South) 41km (-41). Total Y = 77 - 36 - 41 = 0 km.
Calculate Net Horizontal Displacement (East-West)
Start X = 0. Move East 34km (+34), then move West 65km (-65). Total X = 34 - 65 = -31 km. Since the position is -31km (31km West of origin Y), Keval must travel 31km East to return to point Y.
B: 29km West is incorrect as the calculated displacement is 31km, not 29km; C: 30km East is mathematically incorrect; D: 33km North is wrong as the net vertical displacement is zero.
A is correct because the net horizontal displacement is 31km West, requiring a travel of 31km East to return to the starting point Y.
Always assign North/East as positive and South/West as negative coordinates to solve complex direction problems in seconds without drawing elaborate diagrams.
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