Two-dimensional Motion and Vectors Projectile Motion Chapter 3: Section 3

Learning Targets Recognize examples of projectile motion Describe the path of a projectile as a parabola Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion P2.2g, P3.4e,

Two-Dimensional Motion When an object is propelled into the air in a direction other than straight up or down, the velocity, acceleration and displacement of the object do not all point in the same direction To solve problems involving projectiles , the motion of the object must be broken down into its x and y components

Components simplify projectile motion When a long jumper approaches his jump, he runs along a straight line, the x-axis. When he jumps, his velocity has both horizontal and vertical components

What are Projectiles? Objects that are thrown or launched into the air and are subject only to the force of gravity are called projectiles A projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity. Examples include softballs, footballs, and arrows

What about an Upward force? A force is not required to keep an object in motion. A force is only required to maintain an acceleration. In the case of a projectile that is moving upward, there is a downward force and a downward acceleration. As the object moves upward it slows down. As the object moves downward it speeds up.

Projectiles follow parabolic trajectories The path of a projectile is a curve called a parabola

Horizontal Motion of Projectiles If an object has an initial horizontal velocity, there will be horizontal motion throughout the flight of the projectile This horizontal velocity can be considered constant if there is no air resistance With air resistance, a projectile slows down as it collides with air particles

Vertical Motion of Projectiles Projectile motion is simply free fall with an initial horizontal velocity If the projectile rises towards a peak, it’s free fall acceleration slows down (19.6 m/s to 9.8 m/s to 0 m/s) As a projectile falls, it speeds up (0 m/s to -9.8 m/s to -19.6 m/s to ...).

Note that the horizontal velocity is constant

The most important concepts about projectile motion are that horizontal velocity remains constant during the course of the trajectory and vertical velocity changes by 9.8 m/s every second (free fall acceleration)

Why do these balls fall at the same rate? Even though the red ball has no initial horizontal velocity, both balls have identical vertical velocity and are subject to free fall acceleration

Review of Projectile Motion Projectiles are objects that when thrown or launched into the air are subject only to the force of gravity The horizontal motion of a projectile will remain constant A force is not required to keep an object in motion; only to cause and acceleration The vertical motion of a projectile is influenced by free fall acceleration a = - 9.8 m/s2

Projectile Motion Equations Vertical Motion of a Projectile that Falls From Rest vy,f = ay∆t vy,f2 = 2ay∆y ∆y = ½ ay(∆t)2

Projectile Motion Equations Horizontal Motion of a Projectile ∆x = vx∆t

Sample Problems The Royal Gorge Bridge in Colorado rises 321 m above the Arkansas River. Suppose you kick a rock horizontally off the bridge. The magnitude of the rock’s horizontal displacement is 45.0 m. Find the speed at which the rock was kicked A baseball rolls off a 0.70 m high desk and strikes the floor 0.25 m away from the base of the desk. How fast was the ball rolling?

Animation: Projectile Motion http://zamestnanci.fai.utb.cz/~schauer/PhE T- 1.0/simulations/simsa79a.html?sim=Projectil e_Motion Look at effect of air resistance, mass (with and without air resistance), angle