Projectile Motion

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

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!

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

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

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

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

*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

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)

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

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

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!

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