Rohit walked 25 m towards south. Then he turned to his left and walked 20 m.…
Rohit walked 25 m towards south. Then he turned to his left and walked 20 m. He then turned to his left and walked 25 m. He again turned to his right and walked 15 m. At what distance is he from the starting point and in which direction?
Answer: A. 35 m East — Concept: In a direction-sense problem, plot the walk on a compass grid with North up. A left turn rotates the heading one quarter-turn counter-clockwise…
- A.
35 m East
- B.
35 m North
- C.
30 m West
- D.
45 m East
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept: In a direction-sense problem, plot the walk on a compass grid with North up. A left turn rotates the heading one quarter-turn counter-clockwise (South to East to North to West to South), and a right turn rotates it one quarter-turn clockwise. The net displacement is found by summing the North-South component and the East-West component of every leg separately; when a component's positive and negative parts are equal, they cancel completely, leaving displacement only along the other axis.
Application:
Start at O and walk 25 m South to reach point B.
At B, turn left; a left turn from South points East. Walk 20 m East to reach point C.
At C, turn left again; a left turn from East points North. Walk 25 m North to reach point D.
At D, turn right; a right turn from North points East. Walk 15 m East to reach point E.
The first leg (25 m South) and the third leg (25 m North) are equal and opposite, so they cancel exactly, leaving no net North-South displacement. The remaining two legs (20 m East and 15 m East) both point the same way and add up to 35 m East.
Cross-check: Placing O at the origin (0, 0): B = (0, -25), C = (20, -25), D = (20, 0), E = (35, 0). The straight-line distance OE is 35 m, lying along the positive x-axis, i.e., due East, confirming the running total above.
