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Sandeep starts walking towards the north from a point and walks 30 m. He turns to the right and walks 30 m. He turns to the left and walks 20 m. He turns to the left and walks 30 m. Finally, he turns to the left and walks 30 m. How far is he now from the starting point? (All turns are 90 degrees turns only unless specified.)
20 m
10 m
15 m
30 m
20 m
Map the movements on a Cartesian plane (X, Y); net movement is the result of cancelling opposite directions (North vs South, East vs West).
Map the movements on a Cartesian plane (X, Y); net movement is the result of cancelling opposite directions (North vs South, East vs West).
Mapping movements to coordinates
Starting at (0, 0). Move North 30m: (0, 30). Turn Right (East) 30m: (30, 30). Turn Left (North) 20m: (30, 50). Turn Left (West) 30m: (0, 50). Turn Left (South) 30m: (0, 20).
Calculating final distance
The final coordinate is (0, 20). The distance from the starting point (0, 0) to (0, 20) is calculated using the magnitude formula sqrt((x2-x1)2 + (y2-y1)2), which is sqrt(0┬▓ + 20┬▓) = 20m.
B: 10m is incorrect as it ignores the final displacement calculation. C: 15m is an arbitrary value not derived from the steps. D: 30m incorrectly assumes the net vertical displacement is 30m without accounting for all turns.
A is correct because the cumulative coordinate tracking confirms a final vertical displacement of 20m north from the starting point.
For direction problems, always use a simple Cartesian grid (X, Y) to avoid visual confusion; North/East are positive, South/West are negative.
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