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A man walks 5 km East, then turns right and walks 3 km, then turns right and walks 5 km. How far is he from the starting point?
3 km
5 km
8 km
13 km
3 km
Visualize the path as a rectangle: he walks 5 km East, turns 90 degrees right to walk 3 km South, and turns 90 degrees right again to walk 5 km West, effectively closing the width of the rectangle.
Visualize the path as a rectangle: he walks 5 km East, turns 90 degrees right to walk 3 km South, and turns 90 degrees right again to walk 5 km West, effectively closing the width of the rectangle.
Coordinate mapping
Starting at (0,0), he walks 5 km East to reach (5, 0). Turning right (South) for 3 km, he reaches (5, -3). Turning right again (West) for 5 km, he reaches (5-5, -3) = (0, -3).
Calculating displacement
His final position is (0, -3). The distance from the starting point (0, 0) to (0, -3) is the absolute value of the change in y-coordinate, which is 3 km.
B: 5 km is incorrect as it is the horizontal distance walked in one segment, not the net displacement; C: 8 km is the total distance traveled (5+3+5), not displacement; D: 13 km is not a result of any combination of these vectors.
A is correct because the path forms three sides of a rectangle where the East and West movements cancel each other out, leaving only the 3 km Southward displacement.
In direction problems, always track horizontal (East/West) and vertical (North/South) movements separately to find the net displacement using the Pythagorean theorem if necessary.