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Recall that a vector has both:

VECTORS. Recall that a vector has both:. Direction. Magnitude. The sum of two vectors is considered the resultant vector. +. Vector A. Vector B. A + B = R. Graphical Method. You must add vectors from head. head. to tail. tail. so. +. Vector B. Vector A. equals. Vector R.

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Recall that a vector has both:

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  1. VECTORS Recall that a vector has both: • Direction • Magnitude

  2. The sum of two vectors is considered the resultant vector + Vector A Vector B A + B = R

  3. Graphical Method You must add vectors from head... head to tail... tail so...

  4. + Vector B Vector A equals Vector R

  5. For Example: A man walks 275m due east then another 125 m due east. What is his resultant displacement?

  6. A man walks 275m due east then another 125 m due east. What is his resultant displacement? PART 1 PART 2 275 m 125 m Using a ruler you measure from the beginning of part 1 to the end of part 2

  7. RULER A man walks 275m due east then another 125 m due east, what is his resultant displacement? PART 1 PART 2 275m 125m

  8. RULER A man walks 275m due east then another 125 m due east. What is his resultant displacement? 275m 125m

  9. RULER = RESULTANT 400m 275m 125m

  10. RESULTANT: 400m East

  11. A man walks 275m due east then another 125 m due west. What is his resultantdisplacement?

  12. A man walks 275m due east then another 125 m due west. What is his resultant displacement? PART 1 275 m

  13. A man walks 275m due east then another 125 m due west. What is his resultant displacement? PART 2 125 m Using a ruler, measure from the beginning of part 1 to the end of part 2

  14. RULER A man walks 275m due east then another 125 m due west. What is his resultant displacement?

  15. RULER A man walks 275m due east then another 125 m due west. What is his resultant displacement? 275m 125m

  16. RULER = RESULTANT 150m 275m 125m

  17. RESULTANT: 150m East

  18. A man walks 275m due east, then another 125 m due north. What is his resultantdisplacement?

  19. A man walks 275m due east then another 125 m due north. What is his resultant displacement? N PART 2 125 m PART 1 E 275 m

  20. Using a ruler you measure from the beginning of part 1 to the end of part 2 125 m PART 2 PART 1 275 m E N

  21. RULER E

  22. RULER N E

  23. 302m = N RESULTANT E

  24. Now we have the magnitude of the resultant vector we need a direction for the resultant vector so… We get our protractors out and measure the angle of the resultant vector

  25. 302m = N RESULTANT 24.4° E

  26. Resultant Vector 302 m; 24.4° North of East

  27. ANGLE NOTATION On the last one we wrote 40° “North of East”, b/c we were saying it went 40° North “from” East. In your notebook try the following for practice

  28. N W E S 30°

  29. ANSWER: 30° East of North

  30. N W E S 30°

  31. ANSWER: 30° South of East

  32. N W E S 30°

  33. ANSWER: 30° East of South

  34. N W E S 30°

  35. ANSWER: 30° West of South

  36. N W E S 30°

  37. ANSWER: 30° South of West

  38. N W E S 30°

  39. ANSWER: 30° North of West

  40. N W E S 30°

  41. ANSWER: 30° West of North

  42. What direction is a vector directed “northeast” or “southwest”?

  43. What direction is a vector directed “northeast” or “southwest”? • By definition, “northeast”, “southeast”, “southwest”, and “northwest” are vectors directed at 45 degrees.

  44. Not only can we add vectors graphically, we can also find the resultant mathematically…

  45. When vectors are added at right angles to each other, the Pythagorean Theorem can be used to determine the magnitude of the resultant. Trigonometric functions can be used to determine the direction.

  46. A plane travels at 450 km/h due north with a wind blowing at 120 km/h due east. What is the resultant velocity of the plane? 120 km/h 450 km/h

  47. 120 km/h 450 km/h tan = 120/450 R = 466 km/h 15 east of north

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