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Anoop starts from Point X and walks 15 m towards North. He then takes a left turn, walks 8 m, turns left again and walks 20 m. He then takes a right turn and walks 5 m, finally taking a right turn and walking 5 m to stop at Point Y. What is the shortest distance between Point X and Point Y, and in which direction is Point Y with respect to Point X?
13 m, West
15 m, North-West
13 m, East
12 m, West
13 m, West
Track net displacement on X (East-West) and Y (North-South) axes separately, then use the Pythagoras Theorem: distance = sqrt(netX┬▓ + netY┬▓).
Track net displacement on X (East-West) and Y (North-South) axes separately, then use the Pythagoras Theorem: distance = sqrt(netX┬▓ + netY┬▓).
Coordinate Mapping
Starting at X(0,0): 1. Move North 15m (0, 15). 2. Left (West) 8m (-8, 15). 3. Left (South) 20m (-8, -5). 4. Right (West) 5m (-13, -5). 5. Right (North) 5m (-13, 0).
Calculate Shortest Distance
Final point Y is at (-13, 0). The distance from origin X(0,0) to Y(-13,0) is simply the magnitude of the horizontal displacement, which is 13m.
Determine Direction
Since point Y(-13, 0) is purely on the negative X-axis relative to X(0,0), the direction is West.
B is wrong because the resultant position is strictly on the horizontal axis; C is wrong because the total X displacement is to the West, not East; D is wrong because the calculation yields 13m, not 12m.
A is correct because the net horizontal displacement is 13m to the West while the net vertical displacement is zero.
Always draw a quick '+' coordinate system to avoid sign errors when changing directions repeatedly.
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