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Aim: How can we use the parallelogram method of adding vectors?

Aim: How can we use the parallelogram method of adding vectors?. Do Now: Find the resultant of the following vectors through graphical means: 90 m/s South 150 m/s East Scale: 1 cm = 30 m/s. N. W. E. S. N. W. E. S. N. W. E. S. N. W. E. 90 m/s. S. N. W. E. 90 m/s. S.

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Aim: How can we use the parallelogram method of adding vectors?

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  1. Aim: How can we use the parallelogram method of adding vectors? Do Now: Find the resultant of the following vectors through graphical means: 90 m/s South 150 m/s East Scale: 1 cm = 30 m/s

  2. N W E S

  3. N W E S

  4. N W E S

  5. N W E 90 m/s S

  6. N W E 90 m/s S

  7. N W E 90 m/s S

  8. N 150 m/s W E 90 m/s S

  9. N 150 m/s W E 90 m/s S

  10. N 150 m/s W E 90 m/s S

  11. N 150 m/s W E 90 m/s S

  12. N 150 m/s W E 90 m/s S

  13. N 150 m/s W E 90 m/s 5.8 cm x 30 S

  14. N 150 m/s W E 90 m/s 174 m/s S

  15. N 150 m/s W E 90 m/s 174 m/s S

  16. N 150 m/s W E 90 m/s 174 m/s 31° South of East S

  17. N 150 m/s W E 90 m/s Now solve for the resultant mathematically S

  18. N 150 m/s W E 90 m/s (90 m/s)2 + (150 m/s)2 = R2 174.9 m/s = R S

  19. Two people pull on ropes attached to a box – one with a force of 350 N 35° West of South and one with a force of 420 N 45° South of East. Determine the resultant force on the box. Scale: 1 cm = 70 N

  20. N W E S

  21. N W E S

  22. N W E S

  23. N W E S

  24. N W E 35° 350 N S

  25. N W E 35° 350 N S

  26. N W E 35° 350 N S

  27. N W E 35° 350 N S

  28. N W E 45° 35° 420 N 350 N S

  29. N W E 45° 35° 420 N 350 N S

  30. N W E 45° 35° 420 N 350 N S

  31. N W E 45° 35° 420 N 350 N S

  32. N W E 45° 35° 420 N 350 N S

  33. N W E 45° 35° 420 N 350 N S

  34. N W E 45° 35° 420 N 350 N S

  35. N W E 45° 35° 420 N 350 N S

  36. N W E 45° 35° 420 N 350 N S

  37. N W E 45° 35° 420 N 350 N Resultant S

  38. N W E 45° 35° 420 N 350 N Resultant S

  39. N W E 45° 35° 420 N 350 N 8.4 cm x 70 = 588 N Resultant S

  40. N W E 45° 35° 420 N 350 N 588 N Resultant S

  41. N W E 45° 35° 420 N 350 N 588 N 80° South of East Resultant S

  42. N W E 45° 35° 420 N 350 N 588 N 80° South of East Resultant S

  43. N W E 45° 35° θ 420 N 350 N • Now Solve for the magnitude mathematically • Use a derivation of the law of cosines • R2 = a2 + b2 + 2abcosθ • Where θ is the angle between the 2 vectors S

  44. N W E 45° 35° 420 N 350 N R2 = a2 + b2 + 2abcosθ R2 = (350 N)2 + (420 N)2 + 2(350 N)(420 N)cos80 R = 591.6 N S

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