Devika started walking from a point ‘P’ and moved 210 m towards East. Then she…
2023
Devika started walking from a point ‘P’ and moved 210 m towards East. Then she turned to her right and moved 190 m, and then turned to her right and moved 400 m and again turned to her right and moved 200 m to reach a point ‘Q’. What is the direction and shortest distance of point ‘Q’ from point ‘P’?
- A.
West, 200 m
- B.
West, 190 m
- C.
East, 190 m
- D.
East, 200 m
Attempted by 68 students.
Show answer & explanation
Correct answer: B
Key idea: find the net east–west and north–south displacements and then the straight-line distance and direction.
Start: 210 m east
Turn right → 190 m south
Turn right → 400 m west
Turn right → 200 m north (arrive at Q)
Horizontal (east–west):
East = 210 m
West = 400 m
Net = 400 − 210 = 190 m toward the west
Vertical (north–south):
South = 190 m
North = 200 m
Net = 200 − 190 = 10 m toward the north
Straight-line distance from P to Q = sqrt((190)^2 + (10)^2) ≈ 190.26 m.
Direction = arctan(10/190) ≈ 3.0° north of west (i.e., slightly north of due west).
Conclusion: The exact displacement is about 190.26 m toward slightly north of west. Among the given choices, the best match is the answer that states west with a distance of 190 m.