1. Bell Ringer
You throw a football horizontally, and drop a football from the same height and at the same time.
Which will hit the ground first?
PLEASE DO NOT DISCUSS YOUR ANSWER WITH THOSE AROUND YOU!!!!!!!!!

2. Bell Ringer
A bullet is dropped at the same time a second bullet is shot horizontally. Which will collide with the ground first?
Why does this occur?

3. Projectile Motion

4. Vectors Vector: A quantity with direction Represented by arrows
Length = Size of quantity
Points in the direction of vector quantity

5. Adding Vectors Resultant Vector: The sum of two or more vectors
Tail of Vector
Head of Vector
Resultant Vector: The sum of two or more vectors
When adding vectors, always arrange them HEAD to TAIL
Resultant: From the tail of the 1st vector to the head of the last

6. Adding Vectors Graphical Method:
Slide vectors anywhere on the page as long as they maintain their length and direction
The order in which the vectors are combined does not matter

7. Adding Vectors A D C B

8. Adding Vectors R D A B C

9. Adding Vectors A R C D B

10. Bell Ringer
What is the horizontal component of a 15m vector, with a vertical component of 9 m?

11. Wind and Plane in Same Direction
35 mph
350 mph
The plane’s velocity and the wind velocity can be represented by vector arrows

12. Wind and Plane in Same Direction
35 mph
350 mph
The overall velocity of the plane, is the sum of the wind velocity and the original velocity of the plane

13. Wind and Plane in Same Direction
and draw the resultant vector from the tail of the first vector to the head of the second vector
35 mph
350 mph
Align the vectors head to tail

14. Wind and Plane in Same Direction
v = 385 mph
= 385 mph v
35 mph
350 mph
Therefore:
v = vwind + vplane

15. Wind and Plane in Opposite Directions
350 mph
-35 mph

16. Wind and Plane in Opposite Directions
350 mph
-35 mph
350 mph
-35 mph
Align the vectors head to tail:

17. Wind and Plane in Opposite Directions
350 mph
-35 mph v
Therefore:
v = vwind + vplane
v = (-35 mph) mph
v = 315 mph

18. Wind and Plane in Perpendicular Directions
350 mph
35 mph

19. Wind and Plane in Perpendicular Directions
350 mph
35 mph

20. Wind and Plane in Perpendicular Directions
Align the vectors head to tail
35 mph
350 mph

21. Wind and Plane in Perpendicular Directionsv
35 mph
350 mph
Pythagorean Theorem must be used to find the magnitude of v

22. Wind and Plane in Perpendicular Directionsv
35 mph
350 mph
Therefore:
v2 = (vplane)2 + (vwind)2
v2 = (350 mph)2 + (35 mph)2
v = mph

23. Vector Components Part of a vector
x-component: Determines how far horizontally the vector is tilted
y-component: Determines how far vertically the vector is tilted

24. In this case, both components are positive
Vector Components
y-component A
x-component
In this case, both components are positive

25. Bell Ringer
While flying due east at 120 km/h, an airplane is also carried northward at 45 km/h by the wind blowing due north. What is the plane’s resultant velocity?

26. Projectile Motion
Acts only under the influence of gravity and air resistance AND…
Follows a curved, 2-D path

27. x-component
Neglecting air resistance, the horizontal velocity of a projectile remains constant

28. y-component
The vertical component of the velocity of a projectile changes due to gravity
The object accelerates downward
The y-component acts the same as an object in freefall

29. Projectile Motion

30. Projectile Motion
The horizontal component of a projectile is entirely independent from the vertical component of motion
Changing one does not affect the other

31. Projectile Motion
The equations of 1-D motion still apply (dx = vxt and dy = ½ayt2)
NEVER mix x- and y-components in the same equation DON’T MIX
Time is the only scalar quantity in these equations
ONLY time can be used to tie x- and y-components together

32. Projectile Motion
A ball rolls off a level table with a speed of 2.2 m/s. The table is 1.2 meters high. How far away from the base of the table does the ball land?

33. Practice Problem
A soccer ball is kicked horizontally off a 22.0-meter high hill and lands a distance of meters from the edge of the hill. Determine the initial horizontal velocity of the soccer ball.

34. Bell Ringer
A pool ball leaves a 0.60-meter high table with an initial horizontal velocity of 2.4 m/s. Predict the time required for the pool ball to fall to the ground and the horizontal distance between the table's edge and the ball's landing location.

35. Bell Ringer
As a movie stunt car is driven off a cliff which path will it follow?

36. Practice Problem Do this in your notebook. This is not the bell ringer
A beach ball, moving with a speed of m/s, rolls off a pier and hits the water 0.75 m from the end of the pier.   How high is the pier above the water?

37. Bell Ringer
If we were to find the initial velocity of a projectile shot from a perfectly horizontal gun, what things would we have to measure?

38. Bell Ringer
A bullet has a speed of 350 m/sec as it leaves a rifle. If it is fired horizontally from a cliff 6.4 m above a lake, how far does the bullet travel before striking the water?

39. Bell Ringer
Make a hypothesis about which angle above the horizontal that will launch a projectile the farthest distance.
Be sure to record this.

40. Bell Ringer
Answer the two questions on the worksheet on your bell ringer paper.
PLEASE DO NOT DISCUSS YOUR ANSWER WITH THOSE AROUND YOU!!!!!!!!!

41. Bell Ringer
Explain how you will accomplish the following with your catapult.
Put the same amount of energy into the catapult each time.
The ball is released from the same point for each trial.

42. Projectile Motion
At the top of its path, an object has no y-component to its velocity, it moves perfectly horizontally for an instant

43. Projectile Motion
Neglecting air resistance, the path of a projectile is perfectly symmetrical

44. Projectile Motion
With air resistance, the path of a projectile appears squashed

45. Projectile Motion
Varying the angle at which a projectile is launched will change its range
Range: The horizontal distance achieved by a projectile
Hangtime: Total elapsed time during flight of the projectile

46. Projectile Motion Launch angle >45o  Height outweighs range
Launch angle <45o  Range outweighs height
A projectile will reach the same range when launched at angles which add to 90o (complementary angles)

47. Projectile Motion Maximum range is achieved at some middle angle
45o is its own compliment, therefore projectiles launched at this angle achieve maximum range
Note: This is only true when air resistance is neglected

48. Projectile Motion

49. Satellites

50. Satellites

51. Satellites

52. Satellites Fast moving projectiles
The path of a projectile is curved, and so is the surface of the Earth
If thrown at the right speed, the curvature of the trajectory of the object would match the curvature of the Earth

54. Satellites
A satellite is simply a projectile traveling fast enough to fall around the Earth, rather than into it
The speed needed to achieve orbit is 8 km/s or 18,000 mph
With air resistance, ordinary objects would burn up at such great speeds

55. Test Topics Adding Vectors Topics on the Conceptual Review
Horizontal Projectile Motion Problems
Projectile Motion Lab
Anything else talked about after our last test
Chapter 3 in your text