1. CHAPTER 3 3.1 Scalar & Vector Quantities Scalar Quantity = gives magnitude, quantity/how much of something you have. Examples: 30m/s, 50mph, 17N, $20, 100C o

2. Vector Quantity = Magnitude and direction Examples: 30m/s East, 50mph SW, 17N → Vectors are represented by ____? Arrows, Examples……

3. Vectors are drawn to scale Examples:

4. Vector Addition Various Examples:

5. Vector Addition Cont. When graphically adding vectors, the vectors are drawn tip to tail. Examples:

6. School to Home Example Determine the Resultant Vector graphically.

7. Resultant Vector Resultant Vector = The sum of two or more vectors.

11. How are angles measured? The angle of a vector is measured counterclockwise from the positive x- axis. Examples:

12. 3.2 Velocity Vectors A plane is flying East at 700km/h, the wind is blowing East at 50km/h. What is the plane’s velocity? A plane is flying East at 700km/h, the wind is blowing West at 80km/h. What is the plane’s velocity?

13. Examples Cont. A plane is flying East at 700km/h, the wind is blowing South at 1150km/h. What is the plane’s velocity?

14. 3.3 Components of Vectors Vector Resolution = The breaking down of vectors into their x and y components. Example:

15. Example: finding opposite side of right triangle.

16. Vectors are drawn to scale: Examples: Since vectors are drawn to scale, they can simply be measured to determine the magnitude. Examples:

17. 3.4 PROJECTILE MOTION Projectile = Any object that is shot or thrown thereby making gravity the only force acting on the object. If no gravity: Example: Drop a ball vs throw a ball

18. If no gravity: Drop a ball vs throw a ball horizontally

19. With gravity: Drop a ball vs throw a ball horizontally

20. Q: (White Board???) If you drop a ball and throw an identical ball horizontally, releasing each at the exact same time, which will hit the ground first? WHY? Explain in detail. A: both will hit the ground at the same time Demo with tennis balls.

21. Example: Motion Diagram Draw the motion diagram (dots then vectors) for a car accelerating.

22. Example: Motion Diagram Example: Velocity Diagram

23. 3.5 Upwardly Launched Projectiles

24. Upwardly Launched Projectile Velocity Diagram V, V x & V Y V, V x & V Y

25. Maximum Projectile Range White Board ??? What happens as the angle at which the projectile is shot increases? Sketch the various paths as the angle increases. What angle produces the Maximum Range Use phetlab.com

26. Q: Is this the actual path the cannon ball will take? A: No Q: Why? A: Air resistance will alter the path.

27. EQUATIONS Velocity in the vertical direction V = V i + at V Y = V yi + at Is a projectile a “Free Falling” object? Yes  V Y = V yi –gt

28. Equations Cont. Displacement in the vertical direction (d Y ): d = d i + V i t + ½ at 2 d y = d yi + V yi t + ½ a y t 2 Since projectile is Free Falling object d y = d yi + V yi t + ½ (-g)t 2

29. Equations Cont. Displacement in the horizontal direction d = d i + V i t + ½ at 2 d x = d xi + V xi t + ½ a x t 2 Because gravity does not affect velocity in the horizontal direction, velocity remains constant. d x = 0m + V x t + ½ (0)t 2 d = vt d X = v X t

30. Example Problem Bryn drops a rock from a cliff, it takes 4 seconds for the rock to hit the ground. a) What is the velocity of the ball just before it hits the ground? b) How high is the cliff?

31. Draw sketch v Y = V y i + a y t v Y = (-9.8m/s 2 )(4s) v Y = -39.2m/s d y = d yi + v yi t + ½ at 2 d y = ½ (-9.8m/s 2 )(4s) 2 d y = (-4.9m/s 2 )(16s 2 ) d y = -78.4m The rock fell -78.4m  the cliff is 78.4m high

32. 3.6 Fast Moving Projectiles Satellites Drop a RockThrow rock at 5m/s

33. Throw a Rock at 20m/s The rock will go 4 times farther but will fall at the exact same speed/time

34. Throw a rock at 100m/s The rock will travel 20 times farther but will fall at the exact same speed/time

35. Q: If you could get superman to throw an object faster and faster and faster, what would eventually happen to the object? A: the object would become a satellite. Diagram.

37. The object would eventually fall at the same speed as the Earth is turning. Satellites are in constant “Free Fall” they just never hit the ground. Satellites simply fall “around” the Earth, rather than into the Earth.

38. Satellites simply circle the Earth in constant free fall. Examples: Space Shuttle Communications Satellites The Moon (natural satellite)

39. Artificial (man-made) satellites travel at approximately 8km/s at a height greater than 150km above the Earth’s surface. How fast/high is that in mph and miles?

40. 8km 1 mile 3600s 1s X 1.61km X 1hr = 17,888mph 1s X 1.61km X 1hr = 17,888mph 150km 1mi 1 X 1.61km = 93mi above Earth 1 X 1.61km = 93mi above Earth

41. Q: Why so high above the Earth? A: If too close the Earth’s surface there would be enough air resistance to cause the satellite to burn up. Q: Why? A: Friction from the air.  Satellites must travel above the Earth’s atmosphere. Shooting Star??????????