O-LevelAdditional MathematicsVectors in two dimensions4037/21 · May/June 2013 · Q108 Marks
A plane, whose speed in still air is 240kmh⁻¹, flies directly from A to B, where B is 500km from A on a bearing of 032°. There is a constant wind of 50kmh⁻¹ blowing from the west.
- (i)Find the bearing on which the plane is steered.[4]
- (ii)Find, to the nearest minute, the time taken for the flight.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [2] (i) Use of sin rule/cosine rule/resolving with 50, 240 and 58/32/122/148.
- [1] (i) α = 10.2
- [1] (i) Bearing (0)21.8 or (0)22
- [1] (ii) V² = 240² + 50² – 2 × 240 × 50 × cos(angle between P and W, which is 180 - 58 - α)
- [1] (ii) V = 263 awt
- [1] (ii) T = 500 / V
- [1] (ii) 114 or 1 hour 54 mins
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