Maths Quest Maths A Year 12 for Queensland Chapter 5 Navigation WorkSHEET 5.2 5
WorkSHEET 5.2 Navigation Name: ______
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1 /At 10 am, a charter boat records the bearings of a control tower (270˚T) and antenna (225˚T). At 10.20 am, the bearings are tower (315˚T) and antenna (270˚T).
(a) Using the chart, fix the boat’s position at these times.
(b) How far has the boat travelled in 20minutes?
(c) Calculate the speed of the boat.
(d) On what true bearing is the boat travelling? / (a) Construct lines of sight to features and note points of intersection.
(b) Approximately 5.2 n miles measured on the latitude scale.
(d) 180°T
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2 /
In the diagram above, XY = 4 nautical miles. Find:
(a) angle a
(b) angle b
(c) distance YZ. /
(c) The triangle is isosceles, so
YZ = XY = 4 n mile. / 3
3 /
The figure above shows a vessel on a course 010˚T. At 1150 hours, the navigator sights a lighthouse (L) on a bearing 050˚T. At 1220 hours, the angle on the bow has doubled. The speed of the vessel is 15 knots. Find:
(a) the angle on the bow at 1150 hours and 1220 hours.
(b) the distance travelled between the two sightings.
(c) the distance between the vessel and the lighthouse at 1220 hours. / 6
(c) Distance between vessel and lighthouse
= 7.5 n mile.
4 / Find the unknowns in the following triangles.
(a)
(b)
(c)
(d)
/
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5 / A trawler sights a lighthouse marked as Fl(3)14s95 m14 M.
(a) Describe the flashing pattern expected.
(b) What is the range of the light?
(c) How high is the light above sea level?
(d) The angle of elevation of the lighthouse is 1˚. How far, in nautical miles, is the trawler from the lighthouse? / (a) Three short flashes followed by a long period of darkness. This cycle repeats every 14seconds.
(b) 14 n mile
(c) 95 m
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6 / The yacht Dreamtime is at point A at 6.30am
(see the chart below) and is sailing in a true
northerly direction at 10 knots.
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(a) Locate its expected position at:
(i) 0650 hours
(ii) 0700 hours
(iii) 0710 hours.
(b) Determine the bearing of H at 6.30am.
(c) How far is Dreamtime from H at 6.30am? / (a) (i) At 0650 hours, the position is
3.33 n mile north of A.
(ii) At 0700 hours, the position is
5 n mile north of A.
(iii) At 0710 hours, the position is
6.66 n mile north of A.
(b) 40°T
(c) AH is approximately 6.8 n mile measured on the latitude scale.
Questions 7 and 8 refer to the chart of Moreton Bay on pages 286 and 287 of your textbook (also on the CD).
7 / (a) What is the magnetic variation to the nearest minute in this region?
(b) State the position of Cleveland Point on the mainland. (Use base of lighthouse.)
(c) Name the feature at
(27˚S, 153˚ E). / (a) 11°18¢E
(b) 27°30.6¢S, 153°17.4¢E
(c) The wreck Platypus at The Bluff. / 6
8 / Zachary has been fishing at the Bluff at the eastern end of Peel Island. He departs for the FlG3s light at Pelican Banks (bottom right of map) at 2.15 pm.
(a) Find the distance between these two locations.
(b) On what bearing should he travel? (Give both true and compass bearings.)
(c) How long should the trip take at 13knots?
(d) Estimate the ETA at Pelican Banks.
(e) Zac’s boat Wavedancer uses 25 litres of fuel per hour. How much fuel would be used on the trip from the Bluff to Pelican Banks? / (a) Approximately 5.4 n mile measured on the latitude scale.
(b) 177°T, 166°C
(e) 25 litres used in 60 minutes
? used in 25 minutes
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Questions 9 and 10 refer to the map on page289 of your textbook (also on the CD).
9 / (a) Give the position of Nanango.
(b) What is the magnetic variation in this region? (see dotted line.)
(c) Give the height of the highest feature in the 30-by-30-minute square containing Nanango. / (a) 26°40¢S, 152°E
(b) 10.5°E
(c) 2457 feet / 5
10 / A pilot departs Murgon airfield for Kingaroy airport.
(a) State the bearing she will follow (give both true and compass).
(b) What features might be observed by the pilot during this trip? / (a) 183°T, 172.5°C
(b) Several townships — Wondai, Tingoora, Wooroolin, Memerambi. / 4