22. AIM: What are scalars and vectors? DO NOW: Find the x- and y-components of the following line? (Hint: Use trigonometric identities) Home Work: Handout PHYSICSMR. BALDWIN Vectors9/23/2019 100 m 30 0

23. Types of Quantities The magnitude of a quantity tells how large the quantity is. There are two types of quantities: –1. Scalar quantities have magnitude only. –2. Vector quantities have both magnitude and direction.

24. CHECK. Can you give some examples of each? Scalars Mass Distance Speed Time Vectors Weight Displacement Velocity Acceleration

25. Vectors - Which Way as Well as How Much Velocity is a vector quantity that includes both speed and direction. A vector is represented by an arrowhead line –Scaled –With direction

26. Adding Vectors To add scalar quantities, we simply use ordinary arithmetic. 5 kg of onions plus 3 kg of onions equals 8 kg of onions. Vector quantities of the same kind whose directions are the same, we use the same arithmetic method. –If you north for 5 km and then drive north for 3 more km, you have traveled 8 km north.

27. CHECK. What if you drove 2 km South, then got out your car and ran south for 5 km and walked 3 more km south. How far are you from your starting point? Draw a scaled representation of your journey.

28. Addition of Vectors: Resultant For vectors in same or opposite direction, simple addition or subtraction are all that is needed. You do need to be careful about the signs, as the figure indicates.

29. For vectors in two dimensions, we use the tail- to-head method. The magnitude and direction of the resultant can be determined using trigonometric identities. Addition of Vectors in 2D

30. Trigonometric Identities

31. Vectors at 0 o 4.0 N5.0 N R= 9.0 N Vectors at 45 o 4.0 N 5.0 N R= 8.3 N Vectors at 90 o 4.0 N 5.0 N R= 6.4 N

32. Vectors at 135 o 4.0 N 5.0 N R= 3.6 N Vectors at 180 o 4.0 N5.0 N R= 1.0 N

33. https://maps.google.com/maps?oe=UTF- 8&q=map+of+williamsburg+brooklyn&ie=U TF- 8&hq=&hnear=0x89c25bfd06c12a41:0x82 79f2291cc5d76c,Williamsburg,+Brooklyn,+ NY&gl=us&ei=LAxAUoDYBrj94APopIGgD Q&ved=0CCsQ8gEwAA How far are you from your train home?

34. CHECK Do the first five on page 9 & 10 of the work sheet.

35. Using your protractors, draw the following vectors: 1.5 cm @ 30 O 2.10 km @ 45 O 3.7 m @ 110 O 4.100 km/h @ 315 O 5.8 N @ 135 O

36. END

37. Components of Vectors  A Component of a vector is the projection of the vector on an axis.  To find the components of a vector we need to resolve the vector.  The components a x and a y of the vector a can be found using the right triangle

38. PHYSICSMR BALDWIN KINEMATICS: Vectors AIM: How can we ADD vectors? DO NOW: Find & draw the components of the vector given below 1.10 km @ 60 O 10 km 60 O

39. Addition of Vectors: Graphical Methods If the motion is in two dimensions, the situation is somewhat more complicated. Here, the actual travel paths are at right angles to one another; we can find the displacement by using the Pythagorean Theorem.

40. Addition of Vectors:Graphical Methods Adding the vectors in the opposite order gives the same result:

41. Addition of Vectors:Graphical Methods The parallelogram method may also be used; here again the vectors must be “tail-to-tip.”

42. Addition of Vectors: Graphical Methods Even if the vectors are not at right angles, they can be added graphically by using the “tail-to-tip” method.

43. Adding Vectors by Components Any vector can be expressed as the sum of two other vectors, which are called its components. Usually the other vectors are chosen so that they are perpendicular to each other.

44. Adding Vectors by Components If the components are perpendicular, they can be found using trigonometric functions.

45. Adding Vectors by Components Adding vectors: 1. Draw a diagram; add the vectors graphically. 2. Choose x and y axes. 3. Resolve each vector into x and y components. 4. Calculate each component using sines and cosines. 5. Add the components in each direction. 6. To find the length and direction of the vector, use: