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Date	November Example question	Marks available	2	Reference code	EXN.1.AHL.TZ0.7
Level	Additional Higher Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Find	Question number	7	Adapted from	N/A

Question

The position of a helicopter relative to a communications tower at the top of a mountain at time $t$ (hours) can be described by the vector equation below.

$r = (\begin{matrix} 20 \\ - 25 \\ 0 \end{matrix}) + t (\begin{matrix} 4.2 \\ 5.8 \\ - 0.5 \end{matrix})$

The entries in the column vector give the displacements east and north from the communications tower and above/below the top of the mountain respectively, all measured in kilometres.

Find the speed of the helicopter.

[2]

a.

Find the distance of the helicopter from the communications tower at $t = 0$ .

[2]

b.

Find the bearing on which the helicopter is travelling.

[2]

c.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

$|v| = \sqrt{4 . 2^{2} + 5 . 8^{2} + 0 . 5^{2}}$ (M1)

$7.18 (7.1784 \dots) ({kmh}^{- 1})$ A1

[2 marks]

a.

$r = (\begin{matrix} 20 \\ - 25 \\ 0 \end{matrix})$

$|r| = \sqrt{20^{2} + 25^{2}}$ (M1)

$= \sqrt{1025} = 32.0 (32.0156 \dots) (km)$ A1

[2 marks]

b.

Bearing is $arctan (\frac{4.2}{5.8})$ or $90 °- arctan (\frac{5.8}{4.2})$ (M1)

$035.9 ° (35.909 \dots)$ A1

[2 marks]

c.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

Syllabus sections

Topic 3—Geometry and trigonometry » AHL 3.12—Vector applications to kinematics

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