1. Motion in Two-Dimensions
Projectile Motion Notes
January 4, 2017

2. Projectile Motion Projectiles launched horizontally
A projectile can be anything that moves through the air after it has been given an initial “thrust” or input force
Projectiles are only under one force as they move through the air –GRAVITY!
We ignore air resistance in most cases to simply the problems
There are two general categories:
Projectiles launched horizontally
Projectiles launched at an angle

3. Important Facts about Projectile Motion:
Vertical and horizontal motions are independent of each other.
We can relate the height, time in the air, and initial vertical velocity of the projectile by using its vertical motion, then determine the range (x-distance)
We use basic motion equations to solve!

4. Look at the pictures:

5. Horizontal Projectile Motion Demonstrations:

6. Horizontal and Vertical Components of Motion:
Vertical Motion ONLY!
Horizontal Motion ONLY!
Vertical and Horizontal Motion!

7. Horizontal and Vertical Components:
The path of the projectile is known as the TRAJECTORY!
Dx will stand for displacement on the x-axis or in the horizontal direction. This is also known as the range!
Dy will stand for displacement on the y-axis or in the vertical direction. This is also known as the height!
vx will stand for velocity in the horizontal direction.
vy will stand for velocity the vertical direction.

8. Horizontal and Vertical Components:
Starting Point of the Projectile Motion

9. Horizontal and Vertical Components:
x will be positive
y will be positive
vx will be positive
vy will be positive

10. Horizontal and Vertical Components:
x will be positive
y will be positive
vx will be positive
vy will be positive
x will be positive
y will be negative
vx will be positive
vy will be negative

11. Horizontal and Vertical Components:
x will be positive
y will be positive
vx will be positive
vy will be positive
x will be positive
y will be negative
vx will be positive
vy will be negative
x will be negative
y will be negative
vx will be negative
vy will be negative

12. Horizontal and Vertical Components:
x will be negative
y will be positive
vx will be negative
vy will be positive
x will be positive
y will be positive
vx will be positive
vy will be positive
x will be positive
y will be negative
vx will be positive
vy will be negative
x will be negative
y will be negative
vx will be negative
vy will be negative

13. TIME WILL ALWAYS BE POSITIVE!

14. What about the acceleration due to GRAVITY
What about the acceleration due to GRAVITY? (The reason for the “sign” will become clear as we do examples!)
m/s2
m/s2
m/s2
m/s2

15. Projectile Motion Basic Formulas:
Dx = vxi t
Dy = vyit + ½ at2
Where:
Dx is horizontal displacement
Dy is vertical displacement
vxi is horizontal initial velocity
vyi is vertical initial velocity
t is the time in flight
a is the acceleration, usually gravity!

16. This is Splat the Cat
R.I.P
Splat the Cat’s days are numbered….Why??

17. Projectiles Launched Horizontally
Splat the cat is tossed horizontally at 20 m/s
off a cliff that is 50 m high.
How long is the Splat in the air?
b) How far (THE RANGE) from the base of the cliff does Splat land?

18. Problems Solving Strategy
1. Write known and unknown variables
2. Write variables for x and y directions
3. Find TIME first!
What’s missing?
ay = g = -9.81m/s2
y = 0
vyi = 0
ax = 0
vxi = 20 m/s
t = ?
y = -50 m
x= ?
x= 0

19. Your Turn:
A plane that is moving 200 m/s drops a package. The package falls meters to the ground.
Draw a picture and label ALL of the components!
How long was the package in the air?
How far down range (Dx) did the package hit the ground?