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# Chapter 8

## by PhysicsJackson on Jan 31, 2008

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## Chapter 8Presentation Transcript

• 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
• 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’
• 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 |
• Pythagoras’ Theorem For a right-angles triangle a 2 + b 2 = c 2 a b c or hypotenuse
• Find the length of the hypotenuse
• 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)
• 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!
• 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)
• Other Calculations
• We can calculate the components of a vector using trigonometry.
•
• Trigonometry – Finding Angles
• Complete Exercises on worksheet