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Date May Specimen paper Marks available 5 Reference code SPM.2.AHL.TZ0.7
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number 7 Adapted from N/A

Question

Two ships, A and B , are observed from an origin O. Relative to O, their position vectors at time t hours after midday are given by

rA(43)+t(58)

rB = (73)+t(012)

where distances are measured in kilometres.

Find the minimum distance between the two ships.

Markscheme

attempting to find rB − rA for example     (M1)

rB − rA = (36)+t(54) 

attempting to find |rB − rA|     M1

distance d(t)=(35t)2+(4t6)2(=41t278t+45)      A1

using a graph to find the d − coordinate of the local minimum      M1

the minimum distance between the ships is 2.81 (km) (=114141(km))      A1

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3— Geometry and trigonometry » AHL 3.14—Vector equation of line
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Topic 3— Geometry and trigonometry

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