Vectors

1. Vectors Chapter 4

2. Scalar • A quantity with only magnitude

3. Vector • A quantity with both magnitude and direction

4. Vector Tail Head

5. Resultant Vector • The sum of two or more vectors

6. Vector Addition • Two addition methods: • Graphical • Algebraic

7. Graphical Vector Addition • Use the following steps

9. (1) • Draw any one of the vectors with its tail at the starting point or origin

11. (2) • Draw the 2nd vector with its tail at the head of the first vector

13. (3) • Draw the resultant vector from the starting point of the 1st vector to the head of the 2nd

15. (4) • Measure the length of the resultant to determine the magnitude of the vector

16. (5) • Measure the angle to determine the direction of the vector

17. Drill: • An insect crawls 4.0 cm east, then 3.0 cm south. Calculate: • a) distance traveled • b) displacement

18. Practice: • A plane flies 5.0 km west, then 2500 m south. Calculate: • a) distance traveled • b) displacement

19. Drill: • A bug crawls 3.0 cm west, then 40.0 mm south. Calculate: • a) distance traveled • b) displacement

20. Drill: • A plane flies 150 m/s east in a 25 m/s wind blowing towards south. Calculate the plane’s velocity relative to the ground.

21. Review HW • Problems 5 - 10 on page 71

22. Adding Vectors with Opposite Signs • Vector1 + (-Vector2) = Vector1 – Vector2

23. V2 V1 V2 - V1 VR

24. Practice: • A bird flies 25 m west, then 57 m east. Calculate: • a) distance traveled • b) displacement

25. Practice: • A bird flies 14 m west, then 32 m east, then 21 m west. Calculate: • a) distance traveled • b) displacement

26. A boat travels upstream at 10.0 m/s in a river flowing at 2.5 m/s. Calculate the velocity of the boat.

27. Multiple vectors • When adding multiple vectors, just repeat the process of head of first to tail of second etc.

28. Algebraic R B q A

29. Practice: • A car goes 3.0 km west, then 4.0 km south, then 5.0 km north. Calculate: • a) distance traveled • b) displacement

30. Algebraic hyp opp q adj

31. Solving the problem • Sin q = opp/hyp • Cos q = adj/hyp • Tan q = opp/adj

32. Algebraic • R2 = A2 + B2 • if right angle • R2 = A2 + B2 –2ABcos q otherwise

33. A ball rolls 45 m north, then is kicked 60.0 m west. Calculate the distance & displacement of the ball.

34. A ball thrown at 50.0 m/s north from a train moving 50.0 m/s west. Calculate the velocity of the ball.

35. A boat travels at 4.0 m/s across in a river flowing at 3.0 m/s. Calculate the velocity of the boat.

36. A plane travels at 250 m/s south in a 50.0 m/s wind blowing east to west. Calculate the velocity of the plane.

37. A plane travels at 25 m/s south in a 15 m/s wind blowing east to west. Calculate the velocity of the plane.

38. Drill: A snail travels at 9.0 cm south then 15.0 cm west then 6.0 cm south. Calculate the displacement of the snail.

39. Check HW • Problems 11 – 14 • Page 74

40. Vector Resolution • Resolving any vector into its x & y components

41. y-axis Vector = 100 units at 37o N o E 37o x-axis

42. y-axis Determine the x & y components Hypotenuse Opposite side 37o Adjacent side

43. Solving the problem • Sin q = opp/hyp • Cos q = adj/hyp • Tan q = opp/adj

44. Solving the problem • sin q = opp/hyp • opp = hyp x sin q

45. Solving the problem • cos q = adj/hyp • adj = hyp x cos q

46. y-axis Determine the x & y components Hypotenuse = 100 m Opposite side = hyp(sin q) q = 37o Adjacent side = hyp(cos q)

47. Trig Functions • x-component = 100(cos 37o) = 100(0.80) = 80 units • y-component = 100(sin 37o) = 100(0.60) = 60 units

48. Resolve the following vector into polar or x & y components: 150 m/s @ 30o N o E

49. Resolve the following vector into polar or x & y components: 250 N @ 37o E o S

50. Resolve the following vector into polar or x & y components: 7500 N @ 53o