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# Chapter 8

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### Chapter 8

1. 1. Chapter 8 – Mapping Space and Time <ul><li>8.2b – Maps and Vectors </li></ul><ul><li>We will find out: </li></ul><ul><li>How vectors should be written </li></ul><ul><li>How resultant vectors can be calculated </li></ul>
2. 2. <ul><li>What do Vectors tell us? </li></ul><ul><li>We know from last lesson that: </li></ul><ul><li>There is more than one way to get to a destination </li></ul>a b c In this case, a + b = c – THEY ARE THE EQUIVALENT JOURNEY!!! For vectors we are only interested in the end result, not how we get there. This is also known as the resultant . Vectors add by placing them ‘tip to tail’
3. 3. Writing Vectors <ul><li>Vectors are written like this </li></ul><ul><ul><li>a – bold type </li></ul></ul><ul><ul><li>or this a – a line underneath </li></ul></ul><ul><ul><li>or this a – an arrow on top </li></ul></ul><ul><li>These are the NOTATIONS to indicate that a value is a vector and not just a number! </li></ul><ul><li>To indicate the magnitude of a vector, the modulus sign | | is used. ie. </li></ul><ul><li>| a | or | a | or | a | </li></ul>
4. 4. Pythagoras’ Theorem For a right-angles triangle a 2 + b 2 = c 2 a b c or hypotenuse
5. 5. Find the length of the hypotenuse
6. 6. <ul><li>Answers </li></ul><ul><li>1. 10.296 cm (3 d pl) </li></ul><ul><li>2. 3.225 cm (3 d pl) </li></ul><ul><li>3. 15.264 cm (3 d pl) </li></ul><ul><li>4. 102.005 cm (3 d pl) </li></ul>
7. 7. <ul><li>5. In a triangle abc, angle a = 90 degrees, ab = 11.3 cm, </li></ul><ul><li>bc = 15.2 cm. Find ac. </li></ul><ul><li>6. In a triangle abc, angle a = 90 degrees, ab = 14 cm, </li></ul><ul><li>bc = 15 cm. Find ac. </li></ul><ul><li>7. In a triangle abc, angle a = 90 degrees, ab = 0.03 cm, </li></ul><ul><li>bc = 0.05 cm. Find ac. </li></ul><ul><li>8. Miss this one out! </li></ul><ul><li>9. A ship sails 32 nautical miles due north then sails 22 nautical miles due east. How far is it from its starting point ? </li></ul><ul><li>10. The diagonal AC of a rectangle ABCD is 0.67 m long and side Ab is 0.32 m long. How long is side BC ? </li></ul>Draw these and try them!
8. 8. More Answers <ul><li>5. 10.166 cm (3 d pl) </li></ul><ul><li>6. 5.385 cm (3 d pl) </li></ul><ul><li>7. 0.04 cm (2 d pl) </li></ul><ul><li>8. n/a </li></ul><ul><li>9. 38.833 nautical miles (3 d pl) </li></ul><ul><li>10. 0.5886 m (3 d pl) </li></ul>
9. 9. Other Calculations <ul><li>We can calculate the components of a vector using trigonometry. </li></ul>