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A person walks 10 km towards the North, turns left and walks 5 km, turns left again and walks 10 km. How far is he from the starting point?
5 km
10 km
15 km
20 km
5 km
Track net vertical and horizontal displacements; opposite movements in the same axis cancel each other out, leaving only the remaining perpendicular offset.
Track net vertical and horizontal displacements; opposite movements in the same axis cancel each other out, leaving only the remaining perpendicular offset.
Initial North Movement
Starting from the origin (0, 0), walking 10 km North places the person at coordinates (0, 10).
First Turn Left (West)
Turning left from North faces the person West. Walking 5 km shifts the position horizontally to (-5, 10).
Second Turn Left (South)
Turning left again faces the person South. Walking 10 km southward brings the vertical position back to 0, resulting in final coordinates of (-5, 0).
Final Distance Calculation
The straight-line distance from the starting point (0, 0) to the final position (-5, 0) is exactly 5 km.
B: 10 km is just the length of a single vertical segment. C: 15 km results from incorrectly adding parts of the path. D: 20 km incorrectly sums up all individual walking distances (10 + 5 + 10) instead of measuring net displacement.
A is correct because the 10 km North movement and the 10 km South movement cancel each other out vertically, leaving a net horizontal displacement of 5 km.
Always separate total path length from shortest straight-line displacement, and look for symmetrical legs that cancel out vector components.
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