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Anuj walks 6 km towards North, turns right and walks 8 km, then turns right and walks 6 km. What is the shortest distance between his starting point and his current position?
6 km
8 km
10 km
14 km
8 km
Visualize the path as a rectangle; since the person travels equal distances vertically in opposite directions (6 km up, then 6 km down), the remaining horizontal displacement is simply the width of the turn.
Visualize the path as a rectangle; since the person travels equal distances vertically in opposite directions (6 km up, then 6 km down), the remaining horizontal displacement is simply the width of the turn.
Mapping the path
Starting at origin (0,0), Anuj walks 6 km North to reach (0,6). He turns right and walks 8 km East to reach (8,6). Finally, he turns right and walks 6 km South, which brings his coordinate to (8, 6-6) = (8,0).
Calculating displacement
The starting point is (0,0) and the current point is (8,0). The shortest distance is the straight-line gap between (0,0) and (8,0), which is 8 km along the x-axis.
A: 6 km is incorrect as it ignores the 8 km lateral movement. C: 10 km is incorrect as it incorrectly applies the Pythagorean theorem (6-8-10) to a path where net North/South displacement is zero. D: 14 km is incorrect as it is simply the sum of 6 and 8, ignoring the vector direction.
B is correct because the North and South movements cancel each other out, leaving only the 8 km eastward displacement as the shortest distance from the start.
Always track movements on an X-Y plane; if the North and South distances are equal, they cancel out, simplifying the problem to the horizontal distance.
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