Projectile Motion Objective: I will distinguish between the horizontal and vertical components of projectile motion and analyze the factors that influence the motion. PAGE 27

What Is A Projectile? Any object which is projected (launched, thrown, shot) and continues to move due to its own inertia (mass)

What Is A Projectile? Projectiles move in two dimensions have both horizontal and vertical components

The combined motion looks like this: The path is not a straight line but an arc of a parabola.

Horizontal Velocity Component Horizontal velocity is ALWAYS constant This means the initial horizontal velocity equals the final horizontal velocity Why? Gravity DOES NOT work horizontally to increase or decrease the velocity (no outside force)

Vertical Velocity Component Changes due to gravity Projectile does not cover equal displacements in equal time periods. Same as the motion of a freely falling object

Vertical Velocity Component Both the magnitude AND direction change

Combining the Components Together they produce a parabolic trajectory (path)

Factors Influencing Trajectory Launch angle Initial velocity Relative height of launch Trajectory: the flight path of a projectile Three factors influence the trajectory of a projectile: the angle of projection, the projection speed, and the relative height of projection. Understand how these factors interact is useful within the context of a sport both for determining how to best project balls and other implements and for predicting how to best catch or strike projected balls.

Launch Angle Influences shape of the trajectory Perfectly vertical Parabolic Perfectly horizontal Maximum range is at 45° Complementary angles cover the same distance. 30° and 60° 15° and 75° The angle of projection and the effects of air resistance govern the shape of a projectile’s trajectory. Angle of Projection: the direction at which a body is projected with respect to the horizontal In the absence of air resistance, the trajectory of a projectile assumes one of three general shapes, depending on the angle of projection. General shapes Perfectly vertical – projectile follows same path straight up and then straight down again Parabolic – an oblique projection angle (00-900), the trajectory is parabolic Shaped like a parabola Symmetrical, right & left halves are mirror images Perfectly horizontal – at an angle of 00, the trajectory resembles one half of a parabola. Projection angle has direct implications for success in the sport of basketball, since a steep angle of entry into the basket allows a some-what larger margin of error than a shallow angle of entry. In projection situations on a field, air resistance may, in reality, create irregularities in the shape of projectiles, trajectory.

Initial Velocity Influences the: Range (horizontal displacement) Maximum height Time in the air When projection angle and other factors are constant, the projection speed determines the length or size of a projectile’s trajectory. Projection speed: the magnitude of projection velocity For a body that is projected at an oblique angle, the speed of projection determines both the height and the horizontal length of the trajectory. The combines effects of projection speed and projection angle on the horizontal displacement, or range, of the projectile. Range: the horizontal displacement of projectile at landing The third major factor influencing projectile trajectory is the relative projection height. Relative projection height: the difference between projection height and landing height When projection velocity is constant, greater relative projection height translates to longer flight time and greater horizontal displacement of the projectile. A projectile’s flight time is increased by increasing the vertical component of projection velocity or by increasing the relative projection height.

Relative Height of Launch Difference between launch heightand landing height Greater the relative launch height, longer the flight time, greater the displacement. When projection angle and other factors are constant, the projection speed determines the length or size of a projectile’s trajectory. Projection speed: the magnitude of projection velocity For a body that is projected at an oblique angle, the speed of projection determines both the height and the horizontal length of the trajectory. The combines effects of projection speed and projection angle on the horizontal displacement, or range, of the projectile. Range: the horizontal displacement of projectile at landing The third major factor influencing projectile trajectory is the relative projection height. Relative projection height: the difference between projection height and landing height When projection velocity is constant, greater relative projection height translates to longer flight time and greater horizontal displacement of the projectile. A projectile’s flight time is increased by increasing the vertical component of projection velocity or by increasing the relative projection height.

Output Activity A) Draw the path of a projectile with its components (see image to the right) Make sure the magnitude and direction of all vectors is correct. B) Turn the diagram into a MIND MAP. Add in labels, descriptions, key concepts, real-world connections, etc.