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Rohan starts from his house and walks 8 km towards North. He turns right and walks 6 km, then turns right again and walks 8 km. How far is he from his starting point?
14 km
10 km
6 km
8 km
6 km
Visualize the path as a rectangle where the horizontal movement remains unchanged, so the distance from the start is simply the net horizontal displacement after two equal North/South movements.
Visualize the path as a rectangle where the horizontal movement remains unchanged, so the distance from the start is simply the net horizontal displacement after two equal North/South movements.
Mapping the path
Rohan moves North 8 km, turns right (East) for 6 km, and turns right again (South) for 8 km.
Net displacement calculation
The North and South movements of 8 km cancel each other out (8 - 8 = 0). This leaves only the Eastward movement of 6 km as the remaining displacement from the starting point.
A: 14 km is incorrect as it is the total distance walked, not the displacement; B: 10 km is incorrect as it would only be true if the path formed a right-angled triangle, which is not the case here; D: 8 km is incorrect as it represents the vertical distance walked, not the final displacement.
C is correct because the 8 km North and 8 km South movements cancel each other out, leaving a direct horizontal distance of 6 km from the starting point.
In direction problems, always check if movements in opposite directions (North-South or East-West) are equal; if they are, they cancel out, simplifying the problem significantly.
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