Aman walks 1 km towards east and then turns southwards and walks 5 km. Again…
2023
Aman walks 1 km towards east and then turns southwards and walks 5 km. Again he turns to east and walks 2 km. After this he turns to the north and walks 9 km. How far is the man from his starting point?
Answer: A. 5 km — ConceptA route made of perpendicular east–west and north–south movements can be reduced to one net horizontal displacement and one net vertical displacement.…
- A.
5 km
- B.
6 km
- C.
6.5 km
- D.
7 km
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
A route made of perpendicular east–west and north–south movements can be reduced to one net horizontal displacement and one net vertical displacement.
These perpendicular components form a right triangle, so the straight-line distance from the start is found using the Pythagorean theorem.
Application
Take east as positive horizontal movement. The total horizontal displacement is 1 + 2 = 3 km east.
Take north as positive vertical movement. The net vertical displacement is 9 − 5 = 4 km north.
The distance from the starting point is √(32 + 42) = √25 = 5 km.
Cross-check
The net components 3 km and 4 km form the standard 3–4–5 right triangle, confirming a distance of 5 km.