3.4 Projectile Motion

Objectives:•Analyze the motion of an object in free fall.•Solve two-dimensional problems.•Calculate the range of a projectile.

Projectile Defined

A projectile is an object that has been launched in to the air with no capacity to propel itself.

Projectile motion is the movement of a projectile as it travels through the air influenced only by its original velocity and gravitational acceleration. The path of a projectile is parabolic. Examples: a baseball pop fly, a car diving

off a cliff, and water flowing out of a hose.

Components of Projectile Motion

The motion of a projectile can be broken up into components. x-component▪ Velocity is constant▪ sx = vxt

y-component▪ Under the influence of gravity▪ The big 4 kinematic equations apply here

A ball rolling across a table with a constant velocity

If a ball is simply dropped from the edge of a table, it will accelerate toward the ground.

As the ball rolls off the table, it continues its horizontal motion, yet it also accelerated vertically. The result is the curved motion shown.

High speed camera showing the motion of a projectile launched horizontally as it compares to a one that is simply dropped.

Animation showing horizontal and vertical vector components.

Example 1

A ball rolls at a constant speed of 0.700 m/s as it reaches the end of a 1.30 m high table. How far from the edge of the table does the ball land?

Projectiles launched at an angle Projectiles launched horizontally have

no initial vertical velocity (viy = 0). However, projectiles launched and an

angle do have an initial vertical velocity. This vertical component of the initial

velocity can be found with ▪ viy = v sin

The constant horizontal velocity can be found with▪ vx = v cos

Animation of a projectile launched at an angle showing component vectors.

Velocity vectors as a ball kicked into the air travels throughout its trajectory. Blue vectors are vertical components under the influence of the acceleration of gravity. Yellow are the constant horizontal velocity vectors. The red are the resultant vectors.

Example 2

A baseball is hit and moves initially at an angle of 35.0o above the horizontal ground with a velocity of 25.0 m/s. (a) What are the vertical and horizontal components of the initial velocity of the ball. (b) How long will the ball be in the air? (c) What will be the range for this projectile?