1. Projectile Motion

2. Projectile An object that is moving in two directions
The directions are horizontal and vertical
Also called X and Y on a graph
Has a single force that acts upon it - the force of gravity

3. Motion of a projectile
Forces are only required to cause an acceleration (not a motion)
Inertia causes an object to continue to move in a straight line unless acted on by an outside force
There is a downward force and a downward acceleration
If shot upward, the object will be moving upward and slowing down

4. Components of motion
There are two components of motion – horizontal and vertical
Only the vertical motion is affected by gravity
The two components of motion are independent of each other
The object will continue to move horizontally at constant velocity until it hits the ground
The distance the object travels is the velocity times the time in the air
Horizontal distance comes from horizontal velocity, this velocity is constant, so it uses a linear formula. There is no acceleration, so the formula is actually from velocity equals distance divided by time

5. The path is curved Gravity is an acceleration
Acceleration increases velocity
The object moves faster and faster
The object moves a longer and longer distance in a given period of time
The shape given by this type of movement is a parabola
Projectiles travel with a parabolic trajectory due to the fact that the downward force of gravity accelerates them downward from their otherwise straight-line, gravity-free trajectory

6. Two components of motion
The two components are independent, they have to be calculated independently
The initial velocity is a vector, which has a magnitude and a direction
The X and Y components of the initial velocity vector form a right triangle
VX = V cos θ
VY = V sin θ

7. Calculations
Given a velocity and an angle, solve for the distance traveled
Sample problem: V = 35 m/s, θ = 40°
Step 1: VX = V cos θ = 35 cos 40° = 26.8 m/s
Step 2: VY = V sin θ = 35 sin 40° = 22.5 m/s
Distance equals velocity times time
Distance is an X value, use VX or D = VX X t
You still need to calculate time
VX is velocity in the X direction, VY is velocity in the Y direction

8. Calculating time Calculating time is harder, it has two parts
The time it takes to go up
The time it takes to come down
Total time is the sum of both, or
t = t1 + t2
Each of the two times is calculated separately

9. Time One

10. Time One (alternate)

11. t = t1 + t2 = 2.3 s + 2.3 s = 4.6 sec Time Two
Time two comes from the time it takes the object to fall from its peak height
If the object starts at the same height it ends up at, then the time to come down is the same as the time to go up
t = t1 + t2 = 2.3 s s = 4.6 sec
Now you can solve for distance traveled: D = VX X t = 26.8 m/s x 4.6 s = m

12. Time Two continued

13. Calculate distance First calculate total time
t = t1 + t2 = 2.3 s s = 5.68 s
Now calculate distance traveled
D = VX X t = 26.8 m/s x 5.68 s = m

14. Alternate Methods
There are several other ways to work projectile motion problems
One of the ways is to solve for time using a quadratic equation