1. Projectile Motion
AP Physics C

2. What is projectile?
Projectile -Any object which projected by some means and continues to move due to its own inertia (mass).

3. 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

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

5. Thought Question 1:
Suppose you run at constant speed and wish to throw a ball so that you can catch it as it comes back down. In what direction should you throw the ball? UP

6. 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
Vertical

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

8. 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

9. Thought Question 2
As the projectile moves in its parabolic path, is there any point along its path where the velocity and acceleration vectors are (a) perpendicular to each other? (b) parallel to each other?
YES, at the peak
NEVER

10. Thought Question 3
A home run is hit in a baseball game. The ball is hit from home plate into the stands, along a parabolic path. What is the acceleration of the ball (a) while it is rising, (b) at the highest point of the trajectory, and (c) while it is descending after reaching the highest point?
-9.8 m/s^2 down

11. Vertically Launched Projectiles
You will still use kinematic #2, but YOU MUST use COMPONENTS in the equation. vo
voy q
vox

12. 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
15.97 m/s, m/s
q = 53

13. Example
What I know
What I want to know
vox=12.04 m/s t
voy=15.97 m/s
Vfy = m/s
ay=-10m/s^2
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
How long is the ball in the air?
vfy=viy+ayt
-15.97= t
t=3.26 s
3.26 s

14. 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?
x=vixt+1/2axt2
x=12.04(3.26)+1/2(0)(3.26)2
X=39.24 m
What I know
What I want to know x
39.24 m

15. Example What I know What I want to know y
Vfy=0m/s (at peak) y
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?
At the peak, the vertical velocity is 0 m/s
Vfy2=viy 2 +2a y y
(0)2=(15.97)2 +2(-10)y
y=13 m
13.01 m