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Rohan starts from point X and walks 8 km towards North. He turns right and walks 5 km, then turns right again and walks 8 km. How far is he from point X and in which direction?
5 km East
8 km East
5 km West
13 km East
5 km East
Visualize the path as a rectangle: he goes North, turns right (East), then turns right again (South). Since the North and South distances are equal, he is directly East of his starting point by the exact distance of the middle segment.
Visualize the path as a rectangle: he goes North, turns right (East), then turns right again (South). Since the North and South distances are equal, he is directly East of his starting point by the exact distance of the middle segment.
Mapping movement
Starting at X(0,0), he walks 8 km North to reach (0,8). Turning right means facing East, walking 5 km brings him to (5,8). Turning right again means facing South, walking 8 km brings him to (5,0).
Calculating displacement
The final position is (5,0) and the starting point is (0,0). The straight-line distance is 5 km along the X-axis (East direction).
B: 8 km East is incorrect as the distance is defined by the horizontal segment only; C: 5 km West is incorrect as he turned right from North, which leads East; D: 13 km East ignores the geometry of the path and incorrectly sums the segments.
A is correct because the Northward movement of 8 km and the subsequent Southward movement of 8 km cancel each other out, leaving only the 5 km Eastward displacement.
In direction problems, always treat North/South and East/West as opposing vectors; if the distances in opposite directions are equal, they cancel out, leaving the net displacement as the sum of the perpendicular segments.
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