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 S WE

3. N S WE

4. N S WE

5. N S WE 90 m/s

6. N S WE

7. N S WE

8. N S WE 150 m/s

9. N S WE 90 m/s 150 m/s

10. N S WE 90 m/s 150 m/s

11. N S WE 90 m/s 150 m/s

12. N S WE 90 m/s 150 m/s

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

14. N S WE 174 m/s 90 m/s 150 m/s

15. N S WE 174 m/s 90 m/s 150 m/s

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

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

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

21. N S WE

22. N S WE

23. N S WE

24. N S WE 35° 350 N

25. N S WE 35° 350 N

26. N S WE 35° 350 N

27. N S WE 35° 350 N

28. N S WE 35° 350 N 45° 420 N

29. N S WE 35° 350 N 45° 420 N

30. N S WE 35° 350 N 45° 420 N

31. N S WE 35° 350 N 45° 420 N

32. N S WE 35° 350 N 45° 420 N

33. N S WE 35° 350 N 45° 420 N

34. N S WE 35° 350 N 45° 420 N

35. N S WE 35° 350 N 45° 420 N

36. N S WE 35° 350 N 45° 420 N

37. N S WE 35° 350 N 45° 420 N Resultant

38. N S WE 35° 350 N 45° 420 N Resultant

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

40. N S WE 35° 350 N 45° 420 N 588 N Resultant

41. N S WE 35° 350 N 45° 420 N 588 N80° South of East Resultant

42. N S WE 35° 350 N 45° 420 N 588 N80° South of East Resultant

43. N S WE 35° 350 N 45° 420 N Now Solve for the magnitude mathematically Use a derivation of the law of cosines R 2 = a 2 + b 2 + 2abcosθ Where θ is the angle between the 2 vectors θ

44. N WE 35° 350 N 45° 420 N R 2 = a 2 + b 2 + 2abcosθ R 2 = (350 N) 2 + (420 N) 2 + 2(350 N)(420 N)cos80 R = 591.6 N S