O-LevelAdditional MathematicsVectors in two dimensions4037/22 · Oct/Nov 2016 · Q107 Marks
The town of Cambley is 5 km east and p km north of Edwintown so that the position vector of Cambley from Edwintown is (5000 / 1000p) metres. Manjit sets out from Edwintown at the same time as Raj sets out from Cambley. Manjit sets out from Edwintown on a bearing of 020° at a speed of 2.5 m s⁻¹ so that her position vector relative to Edwintown after t seconds is given by (2.5t cos 70° / 2.5t cos 20°) metres. Raj sets out from Cambley on a bearing of 310° at 2 m s⁻¹.
- (i)Find the position vector of Raj relative to Edwintown after t seconds.[2]
- (ii)Find the value of T and of p.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.
- [B1] (i) r_j = ( (5000 - 2t cos40) / (1000p + 2t cos50) ) x coordinate oe
- [B1] y coordinate oe
- [M1] (ii) 2.5tcos70=5000-2tcos40 equate their x values (must be 3 terms)
- [DM1] t = 5000/(2.5cos70+2cos40) make t the subject allow one sign error
- [A1] = 2095 awrt or 2090 or 2100
- [M1] (2.5cos20-2cos50)×2095=1000p equate their y values(must be 3 terms) and insert their t or |t|.
- [A1] p = 2.23 awrt
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