1. Vectors and Scalars
Physics

2. Bell Ringer 10/13/15
Answer the following on your bell ringer sheet:
1. Is displacement a vector or scalar? 2. What is the difference between vectors & scalars?
NB: Don’t forget to write your objective in your notebook before we start.

3. Scalar Scalar Example Magnitude Speed 20 m/s Distance 10 m Age
15 years
Heat
1000 calories
A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it.
Magnitude – A numerical value

4. Vector
A VECTOR is ANY quantity in physics that has BOTH MAGNITUDE and DIRECTION.
Vector
Magnitude & Direction
Velocity
20 m/s, N
Acceleration
10 m/s/s, E
Force
5 N, West

5. Objective
We will use a treasure hunt activity to create a vector addition map
I will map the course taken and add vectors to find the resultant.
3F “ graphical vector addition”

6. Agenda Cornell Notes- Essential Questions Vector treasure hunt
Vector Map

7. Cornell Notes What is a vector? How do we represent vectors?
Essential Questions:
What is a vector?
How do we represent vectors?
How do we draw a vector?
What shows the magnitude?
What shows the direction?
When should vectors be added?
When should vectors be subtracted?
What is the resultant vector?

8. Vectors Vectors Quantities can be represented with; Arrows
Signs (+ or -) 1-D motion
Angles and Definite Directions (North, South, East, West)

9. Vectors Every Vector Tail Head
Vectors are illustrated by drawing an ARROW above the symbol. The head of the arrow is used to show the direction and size of the arrow shows the magnitude

10. Vector Addition
VECTOR ADDITION – If 2 similar vectors point in the SAME direction, add them.
Example: A man walks 54.5 meters east, then another 30 meters east. Calculate his displacement relative to where he started? +
54.5 m, E
30 m, E
84.5 m, E

11. Vector Subtraction
VECTOR SUBTRACTION - If 2 vectors are going in opposite directions, you SUBTRACT.
Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started?
54.5 m, E -
30 m, W
24.5 m, E

12. Resultant
The vector representing the sum of two or more vectors is called the resultant vector.

13. Vector Treasure Hunt
Create directions that lead to a specific object/picture. You must have at least 4 turns.
Generate a map from your origin ( door) to your picture.
Write each direction on an index card.
Scramble the index cards and follow them again.
Then,( tomorrow) Create a vector map of total displacement

14. Compass
Front of room
Front door
Back of room

15. Teacher Model
Directions to object with at least 4 turns from the front door.

16. Create a Map
Map drawn to scale.

17. Example 23 m, E - = 12 m, W - = 14 m, N 6 m, S 20 m, N 35 m, E R
You walk 35 meters east then 20 meters north. You walk another 12 meters west then 6 meters south. Calculate the Your displacement.
23 m, E - =
12 m, W - =
14 m, N
6 m, S
20 m, N
35 m, E R
14 m, N q
23 m, E

18. Vector Map
Resultant
50 ft East
25 ft South

19. Expectation Groups of 3-4 2 minutes to find the picture
10 minutes back track steps and create directions on index cards
2 mins Shuffle cards
Try to locate object from directions.
10 mins draw map to scale

20. Group Pictures Group1- gorilla Group2- snake Group 3- rat
Group 4- eagle
Group 5- alligator
Group 6- chicken
Group 7- pig
Group 8- dog

21. END

22. 10/15/15 Bell Ringer ( 5 minutes!!)
Get back to your groups.
1.On large paper, create a title,
2. Create a map of your directions from origin to picture.
3. Create a Vector map by Summing up the vectors to find the horizontal and vertical components. Draw your resultant.
Write your names & turn in to teacher

23. Example 23 m, E - = 12 m, W - = 14 m, N 6 m, S 20 m, N 35 m, E R
You walk 35 meters east then 20 meters north. You walk another 12 meters west then 6 meters south. Calculate the Your displacement.
23 m, E - =
12 m, W - =
14 m, N
6 m, S
20 m, N
35 m, E R
14 m, N q
23 m, E

24. Bell Ringer 10/15/15 4 minutes
You walked 15 m east from the door, then you walked 6 m south, then you turned around and walked back west 2 m, and another 6 meters west then you walked North 7 m.
Draw a vector diagram to show the motion and find the resultant.

25. Lesson objectives
We will use Pythagorean theorem to find the resultant, horizontal, and vertical components of vectors.
I will resolve a vector into its vertical and horizontal components and find the resultant using Pythagorean theorem.

26. Agenda Bell ringer Problems 1-4 Grade papers
Diagrams only
Pythagorean theorem
( Solve for R)
Grade papers
Right angle triangles & Trig functions
Note: You Need a calculator today & your notebook

27. Vector Addition Worksheet

28. Using Calculators Make sure it is in degrees
Locate the Sin, Cos, & Tan buttons.
Locate the 2nd button.
Locate the Tan-1 Button.

29. Vectors
A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.
Finish
The hypotenuse in Physics is called the RESULTANT.
55 km, N
Vertical Component
Horizontal Component
Start
95 km,E

30. Vectors
A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.
Finish
The hypotenuse in Physics is called the RESULTANT.
55 km, N
Vertical Component
Horizontal Component
Start
95 km,E

31. Vectors
A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.
Finish
The hypotenuse in Physics is called the RESULTANT.
55 km, N
Vertical Component
Horizontal Component
Start
95 km,E

32. BUT……what about the direction?
In the previous example, DISPLACEMENT was asked for and since it is a VECTOR we should include a DIRECTION on our final answer. N
W of N
E of N
N of E
N of W W E
N E
S of W
S of E
NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TOE.
W of S
E of S S

33. Bell Ringer 10/16/15 Its Friday!!!!!
Check your grade in skyward. Write down your current 2nd 6 weeks grade and your semester grade average.
Turn in Bell Ringer sheet.
Remember: Tests must be made up within a week of the test. Monday 10/19 is the deadline. Also late policy is in effect!

34. Agenda Review right angle triangle & Trig functions ( SOH CAH TOA)
How to enter Sin,Cos,Tan examples
How to enter Sin-1,Cos-1, Tan-1 examples
Example problems
How to find missing sides.
How to find missing angles
Complete problems on your own
Note: You Need a calculator today

35. Lesson objectives
We will use trigonometry to find the missing side and the angles from right angle vector diagrams.
I will find the missing angle and missing side using trigonometry: Sine, Cosine, and Tangent functions.

36. Using Calculators Make sure it is in degrees
Locate the Sin, Cos, & Tan buttons.
Locate the 2nd button.
Locate the Tan-1 Button.

37. Using Calculators
Example 1: Use your calculator to find the sin, cos, or tan or any angle.
Example 2: use your calculator to find the angle using the inverse ( Sin-1, Cos-1,& Tan-1)

38. Right angle triangle, 90 Adjacent- Near the angle
Hypotenuse- the longest side
Opposite- opposite the angle

39. What if you are missing a side?

40. Which do I use?

41. What if you are missing a side?
Which will you use to find the missing sides? Pythagorean theorem or SOHCAH TOA?

42. Which do I use?

43. Trig triangles

44. What if you are looking for the angle?
To find the value of the angle we use a Trig function called the Inverse.
Which sides do we have?
Which function do we use?

45. What if you are looking for the angle?
To find the value of the angle we use a Trig function called the Inverse.

46. What if you are looking for the angle?

47. Reviewing the Primary Trigonometric ratios
Worksheet: Lesson 1
Reviewing the Primary Trigonometric ratios

48. Examples

49. What if you are missing a component?
Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components?
The goal: ALWAYS MAKE A RIGHT TRIANGLE!
To solve for components, we often use the trig functions since and cosine.
H.C. = ?
V.C = ? 25
65 m
Let’s identify the sides
SOH- CAH - TOA!!!!

50. What if you are missing a component?
Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components?
The goal: ALWAYS MAKE A RIGHT TRIANGLE!
To solve for components, we often use the trig functions since and cosine.
H.C. = ?
V.C = ? 25
65 m
SOH- CAH - TOA!!!!

51. What if you are missing a component?
Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components?
The goal: ALWAYS MAKE A RIGHT TRIANGLE!
To solve for components, we often use the trig functions since and cosine.
H.C. = ?
V.C = ? 25
65 m

52. BUT…..what about the VALUE of the angle???
Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle.
To find the value of the angle we use a Trig function called the Inverse.
109.8 km
55 km, N q
N of E
95 km,E
So the COMPLETE final answer is : km, 30 degrees North of East

53. BUT…..what about the VALUE of the angle???
Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle.
To find the value of the angle we use a Trig function called the Inverse.
109.8 km
55 km, N q
N of E
95 km,E
109.8 km, 30 degrees North of East

54. BUT…..what about the VALUE of the angle???
Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle. .
109.8 km
55 km, N q
N of E
95 km,E
So the COMPLETE final answer is : km, 30 degrees North of East

55. Example 23 m, E - = 12 m, W - = 14 m, N 6 m, S 20 m, N 35 m, E R
A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement.
23 m, E - =
12 m, W - =
14 m, N
6 m, S
20 m, N
35 m, E R
14 m, N q
23 m, E
The Final Answer: m, 31.3 degrees NORTH or EAST

56. Example
A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north.
8.0 m/s, W
15 m/s, N Rv q
The Final Answer : degrees West of North

57. Example
A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components.
H.C. =? 32
V.C. = ?
63.5 m/s

58. Example
A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement.
1500 km
V.C. 40
5000 km, E
H.C.
5000 km km = km R
964.2 km q
The Final Answer: degrees, North of East km

59. Hmm. That was good.

60. Holy Snakes!!!

61. It’s a bird, it’s a plane, It’s Super Rat!

62. Do I look like I’m playing?

63. Gator’s anyone?

64. Don’t be a chicken??

65. Do you think I’m cute? Yes or Nah? Yessss!!!!

66. What a time to be alive? 