1. Chapter 3 Projectile Motion
Part 1 – Math Rev; intro to Trig and Vectors

2. Math Review or Introduction
Right triangles and trig

3. What is a scalar quantity?
Review…
What is a scalar quantity?
a quantity with magnitude
Start with 8th

4. What is magnitude?
How much of something you have; an amount only; a number

5. What is a vector quantity?
A quantity that has both magnitude and direction

6. Right Triangles One side has a right angle (90°)
The other two angles must add up to 90
Side opposite the right angle is the hypotenuse

7. Right Triangles con’t
Pythagorean Theorem – know 2 sides; find third side

8. Examples 10 ? 15

9. Examples 35 17 ?

10. Examples 50 ?
100

11. Intro to Trig

12. Which side is the h, o and a?

13. 3 Trig functions to find a side when given an angle
NOTE: θ IS THE ANGLE IN DEGREES!

14. SOH CAH TOA (way to remember!)

15. Practice!!!
50° 7 ?

16. Practice!!!
30° ? 5

17. Practice!!!
50° ? 15

18. Practice
25 m
37°
H = ?

19. Trig con’t (finding angles)

20. Finding the angle: use the inverse function
Finding the angle: use the inverse function! (2nd key and then the function)

21. Practice
Find angle A
Find angle B

22. Find side X
Find angle C

23. What a vector can represent:
A drawn vector can be used to represent distance, velocity, acceleration or a force

24. Drawing Vectors… Length of the vector is the magnitude
We use scaled drawings: like a map
Angle and arrow indicate direction
Direction can be in degrees, NSEW, both degrees and NSEW, up or down, left or right

25. Parts of a vector
Tip – ending point (arrow)
Tail – starting point

26. Drawing Vectors…
degrees
90°
40°
180° 0°
360°
270°

27. Drawing Vectors…
degrees
250°

28. Practice Drawing Vectors…
10 cm at 300 degrees
90°
180° 0°
360°
270°

29. Drawing Vectors… Degrees and N, S, E and W
Example: 3 cm at 70° toward S from directly W (S of W)
Put protractor on W and go 70° S
70°

30. Practice – draw a 6 cm vector at 40° towards North from directly E (N of E)
Practice – draw a 4 cm vector at 60° towards E from directly S (E of S)

31. ____° towards _____directly from ___________?
How would you draw 340° ? How can we rename this angle to fit our standard form (note: angle between 0 and 90)
____° towards _____directly from ___________?
START WITH 6TH ON NOV 13

32. Shortening the direction
_____ of ____
Axis you start your measurement from…line up 0 degrees at this axis

33. Rewrite in shortened form….
draw a 5 cm vector at 30° towards North from directly E

34. Drawing Vectors… Example: 3 cm at 70° toward S from directly W
Becomes 3 cm at ____________________________
70°

35. Shortened direction?
Practice – draw a 7 cm vector at 60° towards E from directly S

36. Adding Vectors
Resultant
the __________ of two or more vectors

37. 2 main methods of adding vectors
Head to tail method (aka tip to tail)
Draw first vector
Start next vector where the last one ended (so its tail is connected to the previous vectors tip)

38. Example:
2nd Vector
1st Vector

39. Drawing Resultant
Start where the first vector starts and end where the last vector ends

40. Example:
2nd Vector
Resultant
1st Vector

41. Practice Tip-to-Tail Method

42. Place the following quantities in the appropriate column…are they a scalar or vector quantity?
Time
Acceleration
Distance
Velocity
Displacement
Speed

43. 2nd Method of adding vectors
Tail-to-tail method:
Also known as the Parallelogram Method
Draw the first vector
Draw the second vector starting from the tail of the first vector
Start here with 3rd

44. Drawing the Resultant Form a parallelogram from the two vectors
Do this by drawing lines that are parallel to the two vectors
Resultant starts where the two vectors start and ends in the opposite corner

45. Example: Crosswind
An airplane is flying 80 km/h north is caught in a strong crosswind of 60 km/h blowing from west to east. Will the airplane fly faster or slower than 80 km/h?

46. 60 km/h
80 km/h
80 km/h
Resultant
60 km/h

47. Then we can use the Pythagorean Theorem to find the hypotenuse which is our resultant
A2 + B2 = C2
C = √(A2 + B2)

48. Graphically vs Mathematically adding vectors
Graphically finding the information for vectors is using only a drawing and the measurements
Mathematically is actually adding the numbers
In most cases we will use both methods to double check our answers

49. Problems Involving Vectors

53. PE 1-6 Remember to set a scale!
Be careful with directions! THINK through EACH problem
Include magnitude and direction in your final answer

54. Vector Resolution or resolving the vector
– Breaking the resultant vector into its two vector components
HINT: you are given only ONE vector!

55. Parts of a vector: Vector Components
Component – the two vectors at right angles with one another that are added to form the resultant (the single vector)
(the x and y vectors aka the horizontal and vertical components)

56. To find the x and y: draw parallelogram around the resultant
To find the x and y: draw parallelogram around the resultant! (graphically)
Resultant

57. To find the x and y: mathematically
Resultant