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Date	May 2017	Marks available	5	Reference code	17M.2.SL.TZ2.S_9
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 2
Command term	Find	Question number	S_9	Adapted from	N/A

Question

A ship is sailing north from a point A towards point D. Point C is 175 km north of A. Point D is 60 km north of C. There is an island at E. The bearing of E from A is 055°. The bearing of E from C is 134°. This is shown in the following diagram.

M17/5/MATME/SP2/ENG/TZ2/09

When the ship reaches D, it changes direction and travels directly to the island at 50 km per hour. At the same time as the ship changes direction, a boat starts travelling to the island from a point B. This point B lies on (AC), between A and C, and is the closest point to the island. The ship and the boat arrive at the island at the same time. Find the speed of the boat.

Markscheme

valid approach for locating B (M1)

eg $\,\,\,\,\,$ BE is perpendicular to ship’s path, angle ${\text{B}} = 90$

correct working for BE (A1)

eg $\,\,\,\,\,$ $\sin 46^\circ = \frac{{{\text{BE}}}}{{146.034}},{\text{ BE}} = 146.034\sin 46^\circ ,{\text{ }}105.048$

valid approach for expressing time (M1)

eg $\,\,\,\,\,$ $t = \frac{d}{s},{\text{ }}t = \frac{d}{r},{\text{ }}t = \frac{{192.612}}{{50}}$

correct working equating time (A1)

eg $\,\,\,\,\,$ $\frac{{146.034\sin 46^\circ }}{r} = \frac{{192.612}}{{50}},{\text{ }}\frac{s}{{105.048}} = \frac{{50}}{{192.612}}$

27.2694

27.3 (km per hour) A1 N3

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3—Geometry and trigonometry » SL 3.3—Angles of elevation and depression

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Topic 3—Geometry and trigonometry