1. What is Projectile Motion?

2. Projectile Motion
A projectile is an object moving in two dimensions under the influence of Earth's gravity
Two-dimensional motion of an object
Vertical
Horizontal

3. Types of Projectile Motion
Horizontal
Motion of a ball rolling freely along a level surface
Horizontal velocity is ALWAYS constant
Vertical
Motion of a freely falling object
Force due to gravity
Vertical component of velocity changes with time
Parabolic
Path traced by an object accelerating vertically while moving horizontal

4. 3-7 Projectile Motion
It can be understood by studying the horizontal and vertical motions separately.
Are the same
velocity vector
Path of object
Figure Caption: Projectile motion of a small ball projected horizontally. The dashed black line represents the path of the object. The velocity vector at each point is in the direction of motion and thus is tangent to the path. The velocity vectors are green arrows, and velocity components are dashed. (A vertically falling object starting at the same point is shown at the left for comparison; vy is the same for the falling object and the projectile.)
velocity components 4

5. Examples of Projectile Motion
Launching a Cannon ball
The speed in the x-direction is constant; in the y-direction the object moves with constant acceleration (g) because of gravity.

7. THE COMPONENTS Vertical Question:
Velocity decreases on the way up and increases on the way down (free fall)
And at the top of its path, velocity is what?
Acceleration is the same up and down when you reach the same height
Question:
If you were walking at a constant velocity with a baseball and threw it up in the air while you were walking, would it fall
In front of you
Behind you
Right back in your hands

8. Solving Problems Involving Projectile Motion
Example: Where does the apple land?
A child sits upright in a wagon which is moving to the right at constant speed as shown. The child extends her hand and throws an apple straight upward (from her own point of view), while the wagon continues to travel forward at constant speed.
If air resistance is neglected, will the apple land
behind the wagon
in the wagon
in front of the wagon?
Figure 3-25.
Response: The child throws the apple straight up from her own reference frame with initial velocity vy0 (Fig. 3–25a). But when viewed by someone on the ground, the apple also has an initial horizontal component of velocity equal to the speed of the wagon, vx0. Thus, to a person on the ground, the apple will follow the path of a projectile as shown in Fig. 3–25b. The apple experiences no horizontal acceleration, so vx0 will stay constant and equal to the speed of the wagon. As the apple follows its arc, the wagon will be directly under the apple at all times because they have the same horizontal velocity. When the apple comes down, it will drop right into the outstretched hand of the child. The answer is (b). 8

9. TAKE HOME MESSAGE The X-velocity is independent of the Y- velocity
The speed in the x-direction (horizontal) doesn’t care what the speed in the y- direction (vertical) is!
WHY?

10. REVIEW QUESTION Suppose two balls are released from the same height:
One is dropped from rest the other is thrown horizontally. Which will hit the ground first? Why?

11. Factors Affecting Projectile Motion
What two factors would affect projectile motion?
Angle
Initial velocity
(height – y dist)
(range – x dist)
Initial Velocity
Angle

12. THE FACTORS Angle Initial velocity 0°- 45° = range increases
45° - 90° = range decreases
Initial velocity
Greater initial velocity= farther it will go
The faster it goes horizontally, more ground is covered

13. vxi, vx = Horizontal velocity of a projectile
HORIZONTAL EQUATIONS SYMBOLS
dx= Horizontal displacement (RANGE)
vxi, vx = Horizontal velocity of a projectile

14. dy= vertical displacement (HEIGHT)
VERTICAL EQUATIONS SYMBOLS
Symbols
dy= vertical displacement (HEIGHT)
g = acceleration of gravity (9.81 m/s²)
Vyi = initial vertical velocity (m/s)
Vyf = final vertical velocity (m/s)
Vy = vertical velocity

15. Object Launched Horizontally
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.