Projectile Motion Projectile Motion

What Is Projectile Motion? the motion of objects moving in two dimensions ONLY under the influence of gravity. Air resistance is negligible (we can ignore it). All projectiles display a parabolic shape.

Examples of projectiles include anything launched or thrown into the air or space.

The path of a projectile is called its trajectory. Some Vocabulary The total distance traveled by a projectile is known as its range.

Some Common Misconceptions…. DANGER CLIFF Going fast horizontally means you don’t fall as fast. If you go fast enough, you don’t fall at all. Gravity won’t act on you until you look down.

The Truth Is... If gravity is the only force acting on an object, it will accelerate at a rate of 9.8 m/s2 DOWN, regardless of what’s happening horizontally. In fact, if the object doesn’t have wings, jet engines, propellers or rockets, its horizontal motion will have absolutely no effect on its vertical motion. Horizontal and vertical components are completely independent of each other.

Why? Since gravity is the only force acting on a projectile, and it acts straight down, the acceleration resulting is vertical. There is NO horizontal acceleration, which means that a projectile will maintain constant horizontal velocity as long as it is in the air.

This is Key… Horizontally, projectiles move with constant velocity. ….Because there’s no horizontal force to make it go faster, or slower….Unless we want to talk about air resistance… which we don’t.

Vertically, projectiles move with constant acceleration. ….Because there’s a vertical force, the earth’s gravitational pull, making it accelerate….

Put them together and what do you get?

Horizontal Velocity Determines Horizontal Displacement Only

The Path of a Projectile… Without Gravity Only Equation that you can use: v = d/t The cannon ball moves a constant amount with each second.

Path of a Projectile… With Gravity

The Horizontal Motion is Independent of the Vertical Motion

Projectile Motion Summary Horizontal Motion Vertical Motion Forces Present Acceleration Present Velocity Yes Gravity acting downward No Yes Gravity downward at 9.8 m/s2 No Changing (by 9.8 m/s each second) Constant

Projectile motion is a vector composed of horizontal and vertical components . The x-component of a projectile’s motion is there from the start, and stays the same the entire time. The y-component of a projectile’s motion doesn’t even exist at the beginning, but grows bigger as the object falls. IF LAUNCHED HORIZONTALLY animation

How Do We Solve Projectile Problems?? Consider Horizontal and Vertical Components of Motion Independently Vertical Equations vyf = vyi + gt vyf2 = vyi2 + 2g y y = vyit + 1/2gt2 y = 1/2(vyi+vyf)t Horizontal Equation Vx =  x / t Since horizontal acceleration is zero, this is the only equation. If an initial velocity is given, you must break it into its horizontal and vertical components: Vx = V cos  Vy = V sin 

Draw an accurate diagram showing the trajectory of the object. Solve for the horizontal and vertical components of the initial velocity if given. Identify what you are asked to find. (Remember you need at least 3 pieces of vertical data to use kinematic equations .) If you don’t have 3, look to the horizontal data to find time, which is the only common variable.