17M.2.SL.TZ2.S_9

pestleMathematicsAISLPaper 217M· sl-3-3-angles-of-elevation-and-depressionsource ↗

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 / solution

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]