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Vectors

Vectors. What is the difference between a vector and a scalar number?. Vectors. Scalar. Both have a magnitude but only vectors have a direction. What kinds of things can be represent by vector. Displacement - Magnitude- how far you went Direction - which way. Velocity --

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Vectors

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  1. Vectors What is the difference between a vector and a scalar number?

  2. Vectors Scalar Both have a magnitude but only vectors have a direction

  3. What kinds of things can be represent by vector Displacement- Magnitude- how far you went Direction - which way Velocity -- Magnitude- speed Direction - which way Acceleration -- Magnitude- change in velocity / time Direction - which way Forces Magnitude- how hard you are pushing or pulling Direction - which way

  4. Vectors The direction can be indicated many different ways

  5. If I moved 3 meters and wanted to say which way I could say in terms of common directions Up Right Left Down

  6. North East West South Or I could use compass directions...

  7. 270o 0o 180o 90o Or I could use the angle in degrees...

  8. +y +x -x -y Or I could use Cartesian coordinates

  9. Or I can simply use an arrow to show direction. This is called graphically representing a vector (with a picture) When using a picture, what does the length of the arrow show?

  10. Any way will work but generally one works the best for a given situation. 3 meters to the right 3 meters East 3 meters at 0o Dx = +3 meters 3 meters

  11. Just as scalars can be added 3 apples + 5 apples = 8 apples VECTORS can be ADDED too (but watch direction) 3 + 5 doesn’t always equal 8

  12. WHEN 2 scalar numbers are added, the answer is called the SUM. WHEN 2 Vectors are added, the answer is called the RESULTANT

  13. First we will look at adding vectors which are parallel Are these “vectors” parallel?

  14. 8 m If you walk 3 meters to the right and 5 meters to the right. What would your displacement be? 3 m 5 m 8 meters to the right What is the answer called?

  15. 2 m If you walk 3 meters to the right and 5 meters to the left. What would your displacement be? 3 m 5 m 2 meters to the left 3 + 5 = 2 ????

  16. 2 m If you had used positive and negative x to add these how would you have done it? - x left + x right 3 m + 3 m - 5 m 5 m - 2 m When vectors are parallel, you simply add or subtract the numbers!!!

  17. Vector addition also applies to Velocity (or any other vector for that matter)

  18. Have you ever walked on a moving walkway at an air port? standing still on it walking with it walking against it 3 velocities walkway (relative to..) you relative to walkway you relative to the ground

  19. SCALE = 10 km/hr A plane is flying 60 km/hr North in still air. 60 km/hr

  20. A wind starts blowing at 10 km/hr North, what is the resulting speed of the plane SCALE = 10 km/hr 70 km/hr (resultant) or 70 km/hr NORTH compared to the ground the plane travels at 60 km/hr relative to the air air travels 10 km/hr relative to the ground

  21. What if the plane did a U-turn and pointed south? SCALE = 10 km/hr 50 km/hr (resultant) or 50 km/hr SOUTH 60 km/hr (plane) 10 km/hr (wind)

  22. What would the signs be on the two vectors being added ? SCALE = 10 km/hr + - 60 km/hr + 10 km/hr = -50 km/hr - - 60 km/hr (plane) 10 km/hr (wind) +

  23. SCALE = 10 km/hr -50 km/hr (resultant) or 50 km/hr SOUTH - 60 km/hr + 10 km/hr = -50 km/hr - 60 km/hr (plane) 10 km/hr (wind) +

  24. When vectors point in the same direction. They simply add up!! 6 m 10 m When vectors point in opposite directions, they CANCEL (at least partially) because they have opposite signs 10 m 6 m

  25. A boat can move at 9 m/s in still water. If the water flows at 3 m/s. What will the boat’s velocity be if goes downstream? Upstream?

  26. If you walked 10 m to the East and then 6 m to the East you would be 16 m East from where you started(your displacement) 6 m 10 m 10 m 6 m What if you walked 10 m to the East and then 6 m to the North. Are you 16 m away from where you started?

  27. ADDING NON-Parallel VECTORS to find the resultant

  28. If you walk 10 m East and 6 m North, where would you be? 6 m 10 m When 2 perpendicular vectors are added, use the parallelogram (rectangle) method. 1.) Complete the parallelogram 2.) Draw the resultant from start to finish

  29. What is the resultant Scale 1 dm = 2.24 m 10 m 6 m 6 m 10 m

  30. To specify the resultant we will need to say 2 things about it 10 m 6 m 6 m 10 m Magnitude (from the length of the line and a scale) DIRECTION Measuring an angle with a protractor

  31. Find the resultant: SKIP Scale: 1 dm = 5 m

  32. Find the resultant using the parallelogram method: 8 m West & 19 m South Scale: 1 dm = 5 m Draw the vectors

  33. If the vectors are perpendicular, they form a right triangle. Then we ALSO can use PYTHAGOREAN’s THEORUM to find the RESULTANT

  34. A right triangle has a 90 degree angle. The side opposite it is always the longest side called the hypotenuse Hypotenuse Side Side

  35. Which side is the hypotenuse?

  36. C A B A2 + B2 = C2 This is known as the Pythagorean Theorem

  37. Find the hypotenuse: 3 cm 4 cm 2.5 m 10.5 m

  38. ON the back of your vector WS Use the Pythagorean Theorem to find the resultant for #2. BOX your work below

  39. Find the resultant graphically and using the Pythagorean Theorem : 15 m due south + 25 m due west 1 dm = 5 m SKIP Draw the vectors

  40. A plane plane is flying 75 km/hr due North. A crosswind picks up which blowing 25 km/hr due east. What is the velocity of the plane with the wind (compared to the ground)? What happens to the speed of the plane? Check the answer using the Pythagorean Theorem

  41. Non-perpendicular vectors are added the same way

  42. You can’t simply move an arrow on a piece of paper. It must be carefully redrawn with the same angle and length 90 90 0 0 0 0

  43. You can’t simply move an arrow on a piece of paper. It must be carefully redrawn with the same angle and length

  44. 90 0 0

  45. Find the resultant: 1 dm = 6.3 m

  46. Find the resultant 1 dm = 10 km/hr

  47. Add the following vectors & find the resultant 35 m heading 58o N of E 54 m heading 12o S of W Scale 1 dm = 10 m

  48. VECTOR WS 2

  49. & book problems page 40-41 3, 4, 19, 20, 23, 24

  50. 2 Vectors can be added to make to form their equivalent resultant Resultant =

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