A man walks 12 km towards south and then 7 km towards north. From here he…
2024
A man walks 12 km towards south and then 7 km towards north. From here he walks 5 km towards his left. How far and in which direction is the man with reference to his starting point?
Answer: C. \(5\sqrt{2}\), south-west — ConceptConsecutive movements along the same north-south line combine algebraically: take north as positive and south as negative. Perpendicular horizontal and…
- A.
5km, North-west
- B.
5km, south-west
- C.
\(5\sqrt{2}\), south-west
- D.
\(5\sqrt{2}\), south-east
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Show answer & explanation
Correct answer: C
Concept
Consecutive movements along the same north-south line combine algebraically: take north as positive and south as negative.
Perpendicular horizontal and vertical displacements form a right triangle. Its resultant distance is found with the Pythagorean theorem, and the signs of the components determine the direction.
Application
Let the starting point be (0, 0), with east as positive x and north as positive y.
Walking 12 km south changes the position to (0, -12).
Walking 7 km north changes it to (0, -5), so the man is now 5 km south of the start and is facing north.
While facing north, the left-hand direction is west. Walking 5 km left changes the position to (-5, -5).
The distance from the start is √[(-5)2 + (-5)2] = √50 = 5√2 km. Since both components are westward and southward, the direction is south-west.
Cross-check
The final point is 5 km west and 5 km south of the start. A square with side 5 km has diagonal 5√2 km, confirming the south-west displacement.