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Maths A

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Sue was sailing in the area shown on the chart on 3 March 2013. At 9:00 a.m., she sighted the antenna mast on Wellings Island on a bearing of 180°T. Sue also took a sighting to the lighthouse on Abby Island and found it was at an angle of 098°M.

(i) Sue sighted the antenna mast on a bearing of 180°T. Determine the true bearing from the antenna mast to Sue’s boat.
(ii) Steve was at the lighthouse at 9:00 a.m. on that day. What was (i) the magnetic bearing and (ii) the true bearing from Steve to Sue’s boat?
(iii) Using the information from (i), draw and label a sighting line from the antenna mast. Using the information from (ii), draw and label a sighting line from the lighthouse. Hence find Sue’s position on the chart at 9:00 a.m. Mark this position using the appropriate navigation symbol and label it with the time.

Note: Use the centre of the base of the mast symbol and the centre of the star of the lighthouse symbol as reference points.

c. At 10:50 a.m. on 10 March 2013, a vessel was at 30°30’S 150°E. From here, the vessel travelled on a course of 230ºM for 2 hours at an average speed of 10 knots. When this location was reached the vessel turned onto a heading that would enable it to reach the port at Nadia on Wellings Island.

(i) KP
Given that the variation in this area is 10°E, what was the true bearing for the first leg of this journey? How far had the vessel travelled by 12:50 p.m.? In millimetres, what length on the chart represents this distance travelled?
(ii) KP
Draw the two legs of the vessel’s journey on the chart. Label each of the lines.

(iii) KP
State the location of the vessel at its position near Sunday Island (end of the vessel’s 1st leg).

(iv) MP Level 3
If the vessel had delayed changing course until the second leg could be at 90º to the first leg, how much earlier or later would the vessel have arrived at Nadia assuming that the vessel travelled at an average speed of 10 knots through the whole trip? Give your answer to the nearest minute

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