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A person walks 5 km North, turns East and walks 3 km, then turns South and walks 2 km. How far is he from the starting point?
3 km
4 km
sqrt(18) km
5 km
sqrt(18) km
Calculate net vertical and horizontal displacements from the starting point, then apply Pythagoras theorem to find the shortest distance.
Calculate net vertical and horizontal displacements from the starting point, then apply Pythagoras theorem to find the shortest distance.
Step 1: Track Vertical Displacement
The person walks 5 km North (+5) and then 2 km South (-2). The net vertical displacement is 5 minus 2 equal to 3 km North.
Step 2: Track Horizontal Displacement
The person walks 3 km East (+3). The net horizontal displacement is 3 km East.
Step 3: Calculate Shortest Distance
Using Pythagoras theorem with legs of 3 km and 3 km, the distance from the starting point is the square root of (3 squared plus 3 squared), which equals the square root of 18 km.
A: 3 km is wrong because it only represents a single leg length. B: 4 km is an arbitrary incorrect value. D: 5 km is wrong as it only considers the initial northward movement.
C is correct because the net displacement forms a right-angled triangle with sides 3 km and 3 km, resulting in a distance of square root of 18 km.
Always reduce multi-turn movement into net North-South and East-West components before calculating distance.
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