Lili is facing towards north. She drives 30 km towards north east, 30 km…
2024
Lili is facing towards north. She drives 30 km towards north east, 30 km towards south east, 30 km towards South-west and finally 40 km towards North West. What is her final position with respect to her initial position?
- A.
Same as before
- B.
10 km north-west
- C.
10 km north-east
- D.
10 km south-west
Attempted by 15 students.
Show answer & explanation
Correct answer: B
Solution:
Represent each leg as components (x east, y north). For 45° directions use cos45° = sin45° = 1/√2 ≈ 0.7071.
30 km northeast = (30/√2, 30/√2) ≈ (21.21, 21.21).
30 km southeast = (30/√2, -30/√2) ≈ (21.21, -21.21).
30 km southwest = (-30/√2, -30/√2) ≈ (-21.21, -21.21).
40 km northwest = (-40/√2, 40/√2) ≈ (-28.28, 28.28).
Now sum components: x = 21.21 + 21.21 - 21.21 - 28.28 = -7.07; y = 21.21 - 21.21 - 21.21 + 28.28 = 7.07.
Magnitude = sqrt((-7.07)^2 + (7.07)^2) = sqrt(50 + 50) = sqrt(100) = 10 km.
Direction: x is west (negative) and y is north (positive) → northwest.
Final answer: 10 km north-west of the starting point.