1. Projectile Motion

2. Projectile Motion: Motion in two directions in which the only force on the object is gravityVx Vy
Horizontal Motion (Vx) and Vertical Motion (Vy)

3. v Vector Components vy vx
2 vectors that show how much of the vector is in the x-direction and how much is in the y-direction. v vy vx
Pro Tip: Always draw components as dotted lines to avoid interpreting them as additional vectors!

4. Velocity Trends Vertical Velocity Horizontal Velocity
Acceleration = -9.8 m/s2
Velocity becomes more negative over time due to gravity
Horizontal Velocity
No acceleration in the horizontal direction
No acceleration means…
NO CHANGE IN VELOCITY

5. You are standing outside on a lovely Autumn day in a large, very flat field. You have with you a rifle and two bullets. A question comes to you: What if you shot a bullet horizontally across the field at the exact same time that you dropped the other bullet from the same height? Which bullet would hit the ground first? The dropped bullet, the shot bullet or at the same time?
The Bullet Puzzle

6. This image shows a ball being dropped simultaneously with a ball thrown horizontally
t = 0.1s
Since horizontal and vertical motions are completely independent:
Both balls will hit the ground at the same time!
…REGARDLESS OF Vx
t = 0.2s
t = 0.3s
t = 0.4s
t = 0.5s
t = 0.6s

7. Note: Free Fall is a Special Case of Projectile Motion
Where Vx = 0 (no motion in horizontal direction)
Vyi = 0
Vyi = 0
Vyi = +
Vyi = +

8. *only Vy =0 at max height*
Vertical motion is the same regardless of whether there is motion horizontally
Vy = 0 m/s
*only Vy =0 at max height*
There is still Vx (constant)
Vy = 0 m/s
Vy =
(-)10m/s
Vy = +10m/s
Vy = +10m/s
Vy =
(-)10m/s

9. Projectiles Launched at an Angle
Any projectile launched with an initial velocity (vi) at a certain angle θ can be broken into its X and Y initial velocity components
Vi =
+40 m/s
Vi =
+40 m/s
Vyi
Θ = 55°
Θ = 55°
Vxi
When using equations, you can only use the velocity that corresponds to the proper direction (y direction: Vy …. x direction: Vx)

10. Solving for Initial Vertical Velocities
+40 m/s
Vyi
Θ = 55°
Vxi
Vyi is how fast the object is initially traveling vertically
Vxi is how fast the object is initially traveling horizontally

11. Solving for Projectiles
Horizontal Motion  use constant velocity equation
(since horizontal velocity is constant throughout flight)
Vertical Velocity  use motion equations
(motion is accelerating)

12. Time to Impact Δy Δx vyi vxi t
The time an object spends falling is the SAME amount of time that a projectile is moving forward Δy Δx
vyi
vxi t
Vertical Motion
Horizontal Motion
You can solve for time and use it in the equations for either X or Y!

13. Overview: Main Concepts
Parabolic motion
Initial Vx and Vy found by breaking up resultant into its X and Y components
Vy increases negatively with time
Vx stays the same (neglecting air resistance)
X and Y components are separate
Time is the only common variable