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A person runs 100 meters towards East, then 50 meters towards North, then 100 meters towards West. How far is he from the starting point?
25 meters
50 meters
75 meters
100 meters
50 meters
Track net displacement along horizontal and vertical axes separately. Equal and opposite movements cancel out immediately.
Track net displacement along horizontal and vertical axes separately. Equal and opposite movements cancel out immediately.
Step 1: Initial East Movement
Starting from the origin (0, 0), moving 100 meters towards East places the person at position (+100, 0).
Step 2: North Movement
Moving 50 meters towards North from the current position updates the coordinates to (+100, +50).
Step 3: Final West Movement & Net Distance
Moving 100 meters towards West subtracts 100 from the X-coordinate, bringing the final position to (0, 50). The straight-line distance from the starting point (0, 0) is therefore 50 meters.
A: 25 meters is incorrect as it underestimates the vertical displacement. C: 75 meters is incorrect and does not correspond to any remaining axis calculation. D: 100 meters is incorrect as it mistakenly accounts for a single leg or total distance rather than net displacement from the start.
B is correct because the 100 meters East and 100 meters West cancel each other out horizontally, leaving a net displacement of exactly 50 meters North from the starting point.
Always resolve perpendicular or opposite directional movements independently (East vs West, North vs South) before calculating final straight-line distances.