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Chapter 1

Chapter 1. Vectors. Vectors are arrows. What are these vectors?. 3. 4. Magnitude of a vector = Length of the arrow. What are the magnitudes?. Magnitudes (solution). Adding and subtracting vectors. Add and subtract. Solution. Notations. 4. -3. 5. Vector Components. Terminology.

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Chapter 1

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  1. Chapter 1 Vectors

  2. Vectors are arrows

  3. What are these vectors?

  4. 3 4 Magnitude of a vector= Length of the arrow

  5. What are the magnitudes?

  6. Magnitudes (solution)

  7. Adding and subtracting vectors

  8. Add and subtract

  9. Solution

  10. Notations

  11. 4 -3 5 Vector Components

  12. Terminology

  13. Decomposing a vector Hint: Once you know one side of a right-angle triangle and one other angle, you can find all the lengths using cos, sin or tan.

  14. A quick reminder

  15. Trigonometry

  16. Solution

  17. Check

  18. Angles of a vector Find the angles the four vectors make with the positive x-axis. y 30° x

  19. Calculating the angles

  20. Write down the following three vectors in i j notation. Find the sum of these vectors also. 10o 4.5 5 4 50o 60o

  21. 5 3 4 (-1) times a vector?

  22. 5 4 3 3 4 5

  23. In General

  24. Adding Vectors Diagrammatically You are allowed to move an arrow around as long as you do not change its direction and length. Method for adding vectors: Move the arrows until the tail of one arrow is at the tip of the other arrow. Trace out the resultant arrow.

  25. Subtracting Vectors Diagrammatically

  26. Example

  27. Example

  28. Adding vectors 1 Add the three vectors to find the total displacement.

  29. Adding Vectors 2

  30. Distance & Displacement Distance: How far an object has traveled Displacement (is a vector): How far an object has traveled and in what direction

  31. Distance or Displacement? 5 m 5 m, going East Distance Displacement Distance is actually the magnitude of displacement

  32. 4m Addition of distance / displacement Distance = 4m + 4m = 8m Displacement = 0m

  33. 5m 3m 4m Addition of distance / displacement Distance = 4m + 3m = 7m Displacement = 5m, in the direction of the arrow

  34. Another example Distance = 2m + 4m + 2m + 4m = 12m Displacement = 0m

  35. Distance & Displacement

  36. Scalar & Vector Scalars (e.g. distance, speed): Quantities which are fully described by a magnitude alone. Vectors (e.g. displacement, velocity): Quantities which are fully described by both a magnitude and a direction.

  37. Speed or Velocity? 5 m/s 5 m/s, going East Speed Velocity

  38. Speed = | Velocity | Speed can be interpreted as the magnitude of the velocity vector:

  39. 5 3 4 Summary Three ways to represent a vector: By an arrow in a diagram By i, j components By the magnitude and angle You need to learn all!

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