A person walks 20 meters North from a place. After that he turns right and…
2013
A person walks 20 meters North from a place. After that he turns right and walks 30 meters. After that he turns right and walks 35 meters. After that he turns left and walks 15 meters and then again turning left walks 15 meters. At what distance and in which direction is he from his initial position?
- A.
15 meters West
- B.
30 meters East
- C.
30 meters West
- D.
45 meters East
Attempted by 4 students.
Show answer & explanation
Correct answer: D
Take the starting point as the origin and track the person's coordinates after each leg, using East as positive x and North as positive y. The person begins facing North.
Leg 1 - walks 20 m North: now at (0, 20), facing North.
Leg 2 - turns right (now faces East), walks 30 m: now at (30, 20), facing East.
Leg 3 - turns right (now faces South), walks 35 m: now at (30, -15), facing South.
Leg 4 - turns left (now faces East), walks 15 m: now at (45, -15), facing East.
Leg 5 - turns left (now faces North), walks 15 m: now at (45, 0), facing North.
Final position is (45, 0). The net North-South displacement cancels out (20 North minus 35 South plus 15 North = 0), while the net East-West displacement is 30 + 15 = 45 m East. Hence he is 45 meters East of his initial position.