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Bearings

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CONTENTS

ITEM TYPE NUMBER
Working with maps and angles Workout 40 slides
Angles and bearings Library 10 questions
Once you have registered, you can work through the slides one by one. The workout comprises a series of sides that guide you systematically through the topic concept by concept, skill by skill. The slides may be used with or without the support of a tutor. The methodology is based on problem-solving that advances in logical succession by concept and difficulty. The student is presented with a problem or series of questions, and the next slide presents the fully-worked solution. To use the material you must sign-in or create an account. blacksacademy.net comprises a complete course in mathematics with resources that are comprehensive.

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SAMPLE FROM THE WORKOUT

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SLIDE 1 - QUESTION 1

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SLIDE 2 - SOLUTION

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SAMPLE FROM THE LIBRARY

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QUESTION [difficulty 0.1]

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SOLUTION

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DEPENDENCIES

222: Visual reasoning
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224: Bearings
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226: Working in two dimensions

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CONCEPTS

ITEM
LEV.
Compass points, North, South, West, East 472.1
Sunrise - east, sunset - west 472.1
Sphere 472.3
Earth is a sphere 472.3
Geographical coordinate system 472.3
Latitude and longitude 472.3
Southern and northern sky / hemisphere 472.5
Orientation by position of sun (implicit) 472.6
Zenith 472.7
Standard time, summer time 472.7
Summer / winter solstice 472.8
Spring (vernal) / autumn equinox 472.9
Parallel, meridian, North / South pole 473.0
Stereographic project (implicit) 473.1
Map as a projection 473.6
Mercator projection 473.6
Geographical coordinates 473.7
Clockwise / anticlockwise 473.9
Geometric coordinates from positive x-axis 473.9
Bearing 474.2
Intersection of bearings 474.7
Magnet, North and South poles 475.1
Magnetic monopole (impossible) 475.3
Ferromagnetism 475.3
Earth as a magnet owing to liquid core 475.6
North magnetic pole 475.7
Magnetic compass 475.8
Orienteering 475.8
Magnetic declination 475.8

RAW CONTENT OF THE WORKOUT

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SLIDE 1 The four points of the compass are North, South, West and East The directions of West and East spell the word “WE” ? Find the angle x ? In which direction does the Sun rise? In which direction does the Sun set? What does this tell you about the rotation of the Earth? SLIDE 2 The sun rises in the East and sets in the West. The Earth spins on its own axis from West to East. SLIDE 3 Image: https://commons.wikimedia.org/wiki/File:Azimutalprojektion-schief_kl.jpg The Earth is a sphere. The geographic coordinate system represents positions on the surface of this sphere using lines of latitude and longitude. Latitudes run from East to West. Longitudes run from North to South. SLIDE 4 The geographic coordinate system represents positions on the surface of this sphere using lines of latitude and longitude The latitude running around the middle of the globe dividing it into two hemispheres is called the equator. ? Make a sketch of the globe showing the northern and southern hemispheres. ? You are in the Northern hemisphere in open space and it is morning. How can you tell from the position of the Sun in the sky roughly in which direction you are facing? How would this be different if you were in the Southern hemisphere? SLIDE 5 In the Northern hemisphere the Sun appears in the southern sky. In the Southern hemisphere this is reversed: the Sun appears in the northern sky. You are in the northern hemisphere ? You are facing the rising Sun. Where is North? ? Where is North if you are facing the setting Sun? SLIDE 6 You are in the northern hemisphere. ? You are facing the rising Sun. Where is North? Answer: The Sun rises in the East, so North is on your left. ? Where is North if you are facing the setting Sun? Answer: The Sun sets in the West, so North in on your right. SLIDE 7 The position of the Sun where it is at its highest point is called its zenith. The time of day is midday, noon, 12 pm. The highest point of the Sun in the sky changes as the Earth rotates around the Sun. The diagram shows the path of the Sun in March (Spring). Draw onto this diagram two more curves showing the path of the Sun in December (winter) and June (summer) Notes In the science of astronomy, the Sun does not have a zenith. We use the word “zenith” in the way it is used in common language, and not in astronomy. The time at which the Sun reaches its highest point may not be locally noon, because in some countries standard time is adjusted in the summer to summertime by adding one hour to the clock. This means that instead of the Sun reaching its highest point at 12 noon, it reaches its highest point at 1 p.m. This may also vary from location to location because of time zones. SLIDE 8 For a given location, when the Sun reaches its maximum height in the sky, it is the summer solstice. In the Northern hemisphere the summer solstice occurs on June 21. This is the longest day of the year. When the sun height at noon is its minimum, it is the winter solstice. In the Northern hemisphere the winter solstice occurs on December 21. This is the shortest day of the year. ? What are the summer and winter solstices in the Southern hemisphere? ? The year is divided into four equal parts – winter begins on the day of the winter solstice. What are the names given to the beginning of spring and autumn and in which months do they occur? ? If the Sun is at its highest point on June 21, why is that only the beginning of summer and not the middle of it? SLIDE 9 ? In the Southern hemisphere the summer solstice is December 21 and the winter solstice is June 21. ? The year is divided into four equal parts – winter begins on the day of the winter solstice. What are the names given to the beginning of spring and autumn? The Spring equinox, also called the vernal equinox, marks the beginning of spring and occurs in March. The Autumn equinox marks the beginning of autumn and occurs in September. The exact day varies because the year is not exactly 365 days, and there are Leap Years. ? The Sun’s rays heat the Earth. In summer the heating effect builds up during the summer, and the seasons also reflect the response of nature to the sun. Plants start to grow in spring. Notes The day that each season is said to start varies from country to country, and some countries, because of their location, for example, being on the equator, do not have four seasons. SLIDE 10 Lines of latitude are also called parallels. Lines of longitude are also called meridians. Imagine you are looking down at the Earth from directly above the the North Pole. Draw what you see as you look towards the equator in every direction. Draw all the meridians in increments of 15°. (There are 360° in a circle.) SLIDE 11 The 0° meridian (longitude) is the line that passes from North to South through Greenwich, London. This is by international agreement. SLIDE 12 Parallels are fixed by reference to an angle at the centre of the Earth. Parallels towards the North Pole are marked N. Parallels to towards the South Pole are marked S. You are standing at the North Pole looking towards the equator. Draw what you see and mark ? the 30°N, 60°N parallels ? the 0°, 45°E, 90°E, 135°E, 180°, 45°W, 90°W, 135°W meridians SLIDE 13 SLIDE 14 If the Earth is really a sphere, why does it appear to be flat? SLIDE 15 The Earth is really a sphere but appears to be flat to because it is so large in comparison to a human being. SLIDE 16 It is useful to make a map of the Earth. The spherical shape of the Earth is projected onto a flat surface. There are several different ways in which the spherical shape of the Earth can be made into a map. This image shows the Mercator projection. Image author: Strebe https://commons.wikimedia.org/wiki/File:Mercator_projection_Square.JPG SLIDE 17 Latitude and longitude form a coordinate system. From the map find the coordinates to the nearest 0.5° of ? London ? Liverpool ? Edinburgh ? Belfast SLIDE 18 ? London 51.5°N, 0°W ? Liverpool 53.5°N, 3°W ? Edinburgh 56.0°N, 3°W ? Belfast 54.5°N, 6°W SLIDE 19 Angles can be measured in two directions clockwise or anticlockwise In coordinate geometry it is usual to measure angles from the positive x-axis. SLIDE 20 Use a protractor to measure the above angles to the nearest 1° SLIDE 21 SLIDE 22 In geography, navigation and map work, angles are measured clockwise from the North direction. Such an angle is called a bearing SLIDE 23 Use a protractor to find the above bearings SLIDE 24 SLIDE 25 Find the bearing ? of Edinburgh from Belfast ? of Liverpool from Edinburgh ? of Liverpool from London SLIDE26 ? The bearing of Edinburg from Belfast is 55° ? The bearing of Liverpool from Edinburgh is 180° ? The bearing of Liverpool from London is 312° SLIDE 27 Which city lies on the intersection of a bearing of 330° from London and 105° from Belfast? What the latitude and longitude of this location to the nearest 0.5°? SLIDE 28 Which city lies on the intersection of a bearing of 330° from London and 105° from Belfast? What the latitude and longitude of this location to the nearest 0.5°? Answer: York, with grid coordinates 54°N, 2°W SLIDE 29 Which city lies on the intersection of a bearing of 69° from St. David’s and 174° from Edinburgh? What the latitude and longitude of this location to the nearest 0.5°? SLIDE 30 Which city lies on the intersection of a bearing of 69° from St. David’s and 174° from Edinburgh? What the latitude and longitude of this location to the nearest 0.5°? Answer: Coventry with grid coordinates 52.5°N, 2.5°W SLIDE 31 Magnets have North (N) and South (S) poles Magnets follow the rule that like poles repel, unlike poles attract Complete the following table North South North Repel South SLIDE 32 North South North Repel Attract South Attract Repel SLIDE 33 Magnetic poles are not coloured, but we often paint bar magnets so that the North Pole is red and the South Pole is blue. At the present time, no isolated magnetic pole has been discovered. Any magnet consists of both a North Pole and a South Pole. Effectively, all magnets are bar magnets. Assuming that all magnetic poles are free to move (no friction), for each the above state whether the arrangements of magnets is possible or impossible. SLIDE 34 ? Possible. North and South poles face each other. ? Impossible. South repels South. ? Impossible. Unlike poles repel, and this arrangement also has two isolated North Poles (monopoles) and this has not been discovered in nature. ? Impossible. South repels South. ? Possible. North and South poles face and touch each other. ? Possible. North and South poles face and touch each other. SLIDE 35 The strongest natural form of magnetism arises in ferromagnetic metals. The ferromagnetic metals are iron, cobalt and nickel. The Earth is a giant magnet. Suggest what might explain why the Earth is a magnet. SLIDE 36 Image by Kelvinsong File location: https://commons.wikimedia.org/wiki/File:Earth_poster.svg The Earth is thought to have an outer core made of liquid iron, which is a magnetic material. The rotation of the Earth causes this liquid to flow. When a magnetic material flows, this gives rise to magnetism. SLIDE 37 The Earth has a magnetic north pole. This is not located at the precise place of the geographic north pole. Image source: Wikicommons ? In which direction does the north pole of a magnetic compass point? What is a magnetic compass used for? ? What kind of pole is the North Magnetic Pole? Is it a south pole or a north pole? ? If the North Magnetic Pole is not precisely where the Geographical North Pole is found why doesn’t this make magnitic compasses useless? SLIDE 38 ? In which direction does the north pole of a magnetic compass point? What is a magnetic compass used for? The north pole of a magnetic compass points towars the North Magnetic Pole. Magnetic compasses are used to find directions, for orientation and for navigation. ? What kind of pole is the North Magnetic Pole? Is it a south pole or a north pole? The North Magnetic Pole is magnetically a south pole. The north pole of a magnetic compass points towards it. ? If the North Magnetic Pole is not precisely where the Geographical North Pole is found why doesn’t this make magnetic compasses useless? Accurate maps have a separate arrow pointing in the direction of the Magnetic North Pole. This is called magnetic declination. If you are using a compass to find a direction, you should be able to adjust your compass for this. SLIDE 39 At the foot of a map you see the diagram to the right ? What is the magnetic declination? ? By how many degrees do you adjust the magnetic compass screw that you find on its back? ? Do you adjust the compass East or West? SLIDE 40 ? the magnetic declination is 8° ? You adjust the screw by 8° ? The declination is to the right. You adjust it 8° East.