1. Agenda (10/15) Pick-up guided notes (on front table)
Review relative motion
Notes
Demo
Practice
Physics of Free Fall ride 1

2. Introduction to 2-Dimensional Motion
Use your guided notes to help you follow along with this powerpoint.

3. Click on juggler to link to discovery 3 min video

4. What is a projectile?
Any object that is moving through the air affected only by gravity is called a projectile.

5. Projectile Motion and the Velocity Vector
The path a projectile follows is called its trajectory.

6. Projectile Motion and the Velocity Vector
The trajectory of a thrown basketball follows a special type of arch-shaped curve called a parabola.
The distance a projectile travels horizontally is called its range.
Click on graphic for animation
Vertical drop animation

7. Projectile Motion
Something is fired, thrown, shot, or hurled near the earth’s surface.

8. Which of the following would not be considered projectiles?
A cannonball thrown straight up
A cannonball thrown through the air
A cannonball as it rolls off the edge of a table
All of these are projectiles
(not on your guided notes – a show of hands)
D – all of them are projectiles

9. What are the types of projectiles?

10. 1-Dimensional Projectile (What we have been studying)
Definition: A projectile that moves in a vertical direction only and is subject to acceleration by gravity.
Examples:
Drop something off a cliff.
Throw something straight up and catch it.
You calculate vertical motion only.
The motion has NO horizontal component.

11. 2-Dimensional Projectile
Definition: A projectile that moves both horizontally and vertically, subject to acceleration by gravity in vertical direction.
Examples:
Throw a softball to someone else.
Fire a cannon horizontally off a cliff.
You calculate vertical and horizontal motion.

12. DEMO TIME:
IF YOU LAUNCH A BALL HORIZONTALLY AND DROP A BALL AT THE SAME TIME – WHICH BALL WILL LAND FIRST?

13. What if you increase the speed from which the object is launched
What if you increase the speed from which the object is launched? Will it change the outcome?
Mythbuster version of
Bullet fired versus bullet dropped
Simulation for different angle projectiles

14. How do you account for the results of the demo?
The ONLY force acting on the balls once they are released is gravity.
Once the ball leaves the launcher – there is no other horizontal force that acts upon the ball.

15. Thus, it can be said the acceleration in the horizontal is zero.
This means the initial horizontal velocity equals the final horizontal velocity.
Gravity accelerates objects downwards, but gravity is unable to effect the horizontal velocity of the object.

16. *CRITICAL CONCEPT * Horizontal “Velocity” Component
NEVER changes, covers equal displacements in equal time periods. This means the initial horizontal velocity equals the final horizontal velocity
In other words, the horizontal velocity is CONSTANT. BUT WHY?
Gravity DOES NOT work horizontally to increase or decrease the velocity.

17. Your Turn! Work with a partner to discuss
the questions about this demo.
(5 min.)
Record answers and be prepared to
Share with class.
Dropped and fired marble animation

18. How did you do? #1 Compare and contrast the
horizontal and vertical velocities.
Horizontal velocities are
the SAME throughout.
Vertical velocities INCREASE as
the ball falls. (Each dotted line
represents how far the ball has
fallen after 1 sec.)
Dropped and fired marble animation

19. How did you do? #2 Horizontal acceleration is zero for BOTH balls.
-9.8 m/s/s is constant for both balls.
Dropped and fired marble animation

20. How do you know that the vertical velocity of both balls is greater near the bottom of the figure than it is for the top of the figure? Covers a greater distance in the same time interval.

21. # 4 Gravity only affects the VERTICAL motion
# 4 Gravity only affects the VERTICAL motion. It does not increase or decrease velocity in the horizontal direction. X and y components are perpendicular and INDEPENDENT of one another.

22. The Path of a Projectile (with and without gravity)
Only affects VERTICAL motion

23. Projectiles move in TWO dimensions
Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector.
Horizontal and Vertical
Click here to see animation of components

24. Bellringer (10/16) Take out 2D Projectile motion guided notes
Answer the following in your Bellringer section:
A football player throws the ball down the field. When the ball is at its highest point of its flight:
A. The velocity and acceleration are both zero.
B. The x-velocity and y-velocity are both zero.
C. The x-velocity is non-zero, but the y-velocity is zero
D. The velocity is non-zero, but the acceleration is zero
Physics of Free Fall ride 24

25. Zero Launch Angle Projectiles

26. Launch angle Definition: The angle at which a projectile is launched.
The launch angle determines what the trajectory of the projectile will be.
Launch angles can range from -90o (throwing something straight down) to +90o (throwing something straight up) and everything in between.

27. Zero Launch angle vo
A zero launch angle implies a perfectly horizontal launch.

28. Horizontal and Vertical

29. Projectile Launched Horizontally
Important : GRAVITY only affects the VERTICAL MOTION!!

30. Let’s Summarize:

31. LET’S SUMMARIZE: Vertically Launched Projectiles
NO Vertical Velocity at the top of the trajectory.
Vertical Velocity decreases on the way upward
Vertical Velocity increases on the way down,
Horizontal Velocity is constant
Component
Velocity
Acceleration
Horizontal
Constant
zero
Vertical
Decreases up, top, Increases down
Constant (-9.8 m/s/s)

32. Summary continued… Air resistance is ignored.
Zero launch means perfectly horizontal launch.
Perpendicular components are independent of one another.

33. Key concepts:
Horizontal velocity is constant.
Horizontal acceleration = zero
Vertical velocity changes
Vertical velocity accelerates at a constant rate (-9.8 m/s/s).
Air resistance is ignored.

34. Horizontal Component of Velocity
Once the cannon ball leaves the cannon – what horizontal force acts upon it?

35. Horizontally Launched Projectiles
Projectiles which have NO upward trajectory and NO initial VERTICAL velocity.

36. Horizontal Component of Velocity
Is constant
Not accelerated / acceleration = zero
Not influenced by gravity
WHAT EQUATION DO YOU USE?
Follows equation:
dx = Vi,xt

37. Horizontal and Vertical

39. Vertical Component of Velocity
Changes
Constant acceleration due to ‘g’
WHAT EQUATION DO YOU USE?
Follows equation:
dy = ½ at2

40. Place chairs in rows
Take out ALL notes for hw quiz
Turn in 5 multiple choice questions into top tray
Quiz starts with bell.

41. Vertical “Velocity” Component
NO horizontal component in free fall.
Changes (due to gravity), does NOT cover equal displacements in equal time periods.
Both the MAGNITUDE and DIRECTION change. As the projectile moves up the MAGNITUDE DECREASES and its direction is UPWARD. As it moves down the MAGNITUDE INCREASES and the direction is DOWNWARD.

42. Gravity UNABLE to affect horizontal motion of an object
Gravity UNABLE to affect horizontal motion of an object. The components are perpendicular to one another.

43. dx = vxt dy = 0.5gt2 Object Launched Horizontally horizontal vertical
vx = initial horizontal velocity
dy = initial height
above ground
t = total time in the air
dx = horizontal range
IMPORTANT FACTS
There is no horizontal acceleration.
There is no initial vertical velocity.
The horizontal velocity is constant.
Time is the same for both vertical and horizontal.
horizontal
vertical
dx = vxt
dy = 0.5gt2

44. Horizontally Launched Projectiles
To analyze a projectile in 2 dimensions we need 2 equations. One for the “x” direction and one for the “y” direction. And for this we use kinematic #3.
Remember, the velocity is CONSTANT horizontally, so that means the acceleration is ZERO!
Remember that since the projectile is launched horizontally, the INITIAL VERTICAL VELOCITY is equal to ZERO.

45. Combining the Components
Together, these components produce what is called a trajectory or path. This path is parabolic in nature.
Component
Magnitude
Direction
Horizontal
Constant
Vertical
Changes

46. Horizontally Launched Projectiles
Example: A plane traveling with a horizontal velocity of 100 m/s is 500 m above the ground. At some point the pilot decides to drop some supplies to designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will it land?
What do I know?
What I want to know?
vix=100 m/s
t = ?
y = 500 m
d = ?
viy= 0 m/s
g = -9.8 m/s/s
dx = vixt = (100)(10.1) =
1010 m
10.1 seconds

47. HW – Due block day: Create 5 conceptual concept test questions from the notes. Prepare for quiz - Review relative motion, frame of reference, vectors and projectile motion notes. Complete #1-7

48. What about launches that occur at an angle?

49. Vertically Launched Projectiles
NO Vertical Velocity at the top of the trajectory.
Vertical Velocity decreases on the way upward
Vertical Velocity increases on the way down,
Horizontal Velocity is constant
Component
Magnitude
Direction
Horizontal
Constant
Vertical
Decreases up, top, Increases down
Changes

50. Vertically Launched Projectiles
Since the projectile was launched at a angle, the velocity MUST be broken into components!!! vo
voy q
vox

51. Vertically Launched Projectiles
There are several things you must consider when doing these types of projectiles besides using components. If it begins and ends at ground level, the “y” displacement is ZERO: y = 0

52. Vertically Launched Projectiles
You will still use kinematic #3, but YOU MUST use COMPONENTS in the equation. (scratch out the velocity they’ve given to you as soon as you have done this – NEVER use it in word problem again. (unless it is a component given) vo
voy q
vox

53. Example
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(a) How long is the ball in the air?
(b) How far away does it land?
(c) How high does it travel?
vo=20.0 m/s
q = 53

54. Example 2:
What I know
What I want to know
vox=12.04 m/s
t = ?
voy=15.97 m/s
x = ?
y = 0
ymax=?
g = m/s/s
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(a) How long is the ball in the air?
3.26 s

55. Example
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(b) How far away does it land?
What I know
What I want to know
vox=12.04 m/s
t = 3.26 s
voy=15.97 m/s
x = ?
y = 0
ymax=?
g = m/s/s
39.24 m

56. Example 3: What I know What I want to know t = 3.26 s x = 39.24 m
vox=12.04 m/s
t = 3.26 s
voy=15.97 m/s
x = m
y = 0
ymax=?
g = m/s/s
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(c) How high does it travel?
CUT YOUR TIME IN HALF!
13.01 m

57. YOUR TURN:
Complete : Projectile Motion Practice ws with a group or partner. (1-10)
HW: Physics Fix 15
(1-5)