Chapter 8
- 1. Chapter 8 – Mapping Space and Time 8.2b – Maps and Vectors We will find out: How vectors should be written How resultant vectors can be calculated
- 2. What do Vectors tell us? We know from last lesson that: There is more than one way to get to a destination 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. Writing Vectors Vectors are written like this a – bold type or this a – a line underneath or this a – an arrow on top These are the NOTATIONS to indicate that a value is a vector and not just a number! To indicate the magnitude of a vector, the modulus sign | | is used. ie. | a | or | a | or | a |
- 4. Pythagoras’ Theorem For a right-angles triangle a 2 + b 2 = c 2 a b c or hypotenuse
- 5. Find the length of the hypotenuse
- 6. Answers 1. 10.296 cm (3 d pl) 2. 3.225 cm (3 d pl) 3. 15.264 cm (3 d pl) 4. 102.005 cm (3 d pl)
- 7. 5. In a triangle abc, angle a = 90 degrees, ab = 11.3 cm, bc = 15.2 cm. Find ac. 6. In a triangle abc, angle a = 90 degrees, ab = 14 cm, bc = 15 cm. Find ac. 7. In a triangle abc, angle a = 90 degrees, ab = 0.03 cm, bc = 0.05 cm. Find ac. 8. Miss this one out! 9. A ship sails 32 nautical miles due north then sails 22 nautical miles due east. How far is it from its starting point ? 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 ? Draw these and try them!
- 8. More Answers 5. 10.166 cm (3 d pl) 6. 5.385 cm (3 d pl) 7. 0.04 cm (2 d pl) 8. n/a 9. 38.833 nautical miles (3 d pl) 10. 0.5886 m (3 d pl)
- 9. Other Calculations We can calculate the components of a vector using trigonometry.
- 11. Trigonometry – Finding Angles Complete Exercises on worksheet http://www.funmaths.com/worksheets/downloads/view.htm?ws0036_1.gif
- 13. Relative Velocity Do objects always go where you think that they will? http://www.metacafe.com/watch/39256/crosswinds/