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Rohan starts from home and walks 8 km towards South. He takes a left turn, walks 5 km, turns left again and walks 8 km. He then turns right and walks 3 km. How far is he from his starting point?
8 km
10 km
12 km
15 km
8 km
Track parallel movements: South 8 km followed by North 8 km cancel each other out vertically, leaving only the horizontal displacement of 5 km + 3 km = 8 km.
Track parallel movements: South 8 km followed by North 8 km cancel each other out vertically, leaving only the horizontal displacement of 5 km + 3 km = 8 km.
Initial South Movement
Rohan starts at the home position (0,0) and moves 8 km South to position (0, -8).
First Turn and Movement
Facing South, taking a left turn means he faces East. He walks 5 km to position (5, -8).
Second Turn and Movement
Facing East, taking a left turn means he faces North. He walks 8 km, which completely cancels out the initial 8 km South movement, bringing his vertical coordinate back to 0 at (5, 0).
Final Turn and Distance
Facing North, taking a right turn means he faces East again. He walks 3 km to his final position at (8, 0), making his straight-line distance from home 8 km.
B: 10 km is incorrect because vertical movements cancel out and horizontal total is 8 km. C: 12 km is incorrect as the total horizontal span is 8 km. D: 15 km is incorrect due to incorrect addition of parallel segments.
A is correct because the 8 km South and 8 km North movements completely cancel each other out vertically, leaving a total net horizontal displacement of 5 km + 3 km = 8 km from the starting point.
Always scan for opposite movements of equal magnitude (like North and South of the same distance) to instantly cancel them out and simplify complex path calculations.
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