O-LevelAdditional MathematicsVectors in two dimensions4037/22 · Oct/Nov 2018 · Q126 Marks
A plane that can travel at 260km/h in still air heads due North. A wind with speed 40 km/h from a bearing of 310° blows the plane off course. Find the resultant speed of the plane and its direction as a bearing correct to 1 decimal place.
- A plane that can travel at 260km/h in still air heads due North. A wind with speed 40 km/h from a bearing of 310° blows the plane off course. Find the resultant speed of the plane and its direction as a bearing correct to 1 decimal place.[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] Identifying angle with downward vertical of wind as 50°
- [B1] Triangle drawn with sides 260,40 and included angle of 50°.
- [M1*] Cosine rule : (ν, )² = 260² + 40² – 2 ×260×40cos50°
- [A1] ν,. = 236
- [M1 dep*] Sine rule : sinα/40 = sin50°/ν,
- [A1] α = 7.5°
- [A1] Bearing = 360 - 7.5 = 352.5°
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