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Check in WS 1. Then get out your notebook.

Check in WS 1. Then get out your notebook. Vectors “mathematical objects ” (arrows) that have both magnitude and direction. Example of vector quantities: Displacement Velocity A cceleration. Note: all of these have DIRECTION and SIZE (magnitude). Magnitude

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Check in WS 1. Then get out your notebook.

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  1. Check in WS 1. • Then get out your notebook.

  2. Vectors • “mathematical objects” (arrows) that have both magnitude and direction. • Example of vector quantities: • Displacement • Velocity • Acceleration Note: all of these have DIRECTION and SIZE (magnitude).

  3. Magnitude • the length of a vector (how big it is). • Ex: a velocity of -5m/s has a magnitude of 5m/s and a direction to the left. • Mathematically it means the absolute value. Scalars • quantities that are numerical, but have no direction. • 5 kg (mass), 15 mL (volume) • 20 s (time), -20°C (temperature) • Speed, distance

  4. How to Use a Protractor

  5. Review • Vectors vs. Scalars: what’s the difference? • Discuss your results of randomizing the directions on WS 1 with your group members. Be prepared to share the group’s answers for questions 1-4.

  6. Each leg of the trip is a vector. It has a length and a direction. • Putting together each leg of the trip is the same thing as adding vectors.

  7. No matter what order you use, you still get to your final destination. • The order you add vectors doesn’t matter.

  8. Vector addition is commutative. The order you add them doesn’t matter! • The sum of a bunch of vectors is called the resultant.

  9. Graphically Adding Vectors • The order you add them doesn’t matter. • Connect the vectors “tip to tail.” • (Your next map instruction starts where the other ended.) • The resultant vector is a vector drawn from where you started to where you ended. • START POINT to END POINT

  10. Each group needs a whiteboard, an eraser, a black marker, and a color marker.

  11. Example 1 + = ?

  12. Example 2 = ? + + WRONG

  13. Example 2 = ? + + WRONG

  14. Example 2 = ? + + How do we report the direction of the resultant? An angle by itself is meaningless.

  15. Reporting Angles from the x-axis y Just like math class Positive Angles x -x -y

  16. Reporting Angles from the x-axis y Just like math class Negative Angles x -x -y

  17. If only a degree measurement is given, assume it’s measured from the x-axis, just like you do in math class.

  18. Reporting Angles from Any Axis N W of N E of N N of E N of W E W S of W S of E W of S E of S S

  19. Reporting Angles from Any Axis N W of N E of N N of E N of W E W S of W S of E W of S E of S S

  20. Practice Using a protractor, add the following vectors. Measure the magnitude and direction of the resultant vector. {2.5 cm @ 30° S of E}+ {3 cm @ 75°}

  21. {2.5 cm @ 30° SoE} + {3 cm @ 75°}

  22. {2.5 cm @ 30° S of E} + {3 cm @ 75°}

  23. R=3.2 cm @ 30° {2.5 cm @ 30° SoE} + {3 cm @ 75°}

  24. {2.5 cm @ 30° SoE} + {3 cm @ 75°} R=3.2 cm @ 60° E of N

  25. {1 cm @ 0°} + {2 cm + 90°} + {3 cm @ 180°}

  26. {1 cm @ 0°} + {2 cm + 90°} + {3 cm @ 180°}

  27. {1 cm @ 0°} + {2 cm + 90°} + {3 cm @ 180°} R=2.75 cm 135° 45° 45°

  28. WS 2 for homework • Each table needs to have 4 protractors on it

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