Objectives: The student will be able to:

• Describe what is meant by a projectile.

• Use the kinematics equations of Chapter Two along with the vector component method of Chapter Three to solve problems involving two dimensional motion of projectiles.

• Analyze the motion of a projectile by breaking its velocity and acceleration vectors into vertical and horizontal components.

What is a projectile ?

• A projectile is an object that has only one force acting on it. The singular force acting on the object must be gravity

What are they?

• The definition of a projectile is…

An object that moves through space affected only by gravity.

Projectile Motion and the NFL

• Introduction to Projectile Motion

• http://science360.gov/obj/tkn-video/fc729ef0-22ee-4f61-bb2a-b6c07685fb02/science-nfl-football-projectile-motion-parabolas

Projectile Motion

• Two-dimensional motion of an object– Vertical– Horizontal

Types of Projectile Motion

• Horizontal– Motion of a ball rolling freely

along a level surface– Horizontal velocity is

ALWAYS constant• Vertical

– Motion of a freely falling object

– Force due to gravity– Vertical component of

velocity changes with time• Parabolic

– Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity

Projectile or not?

• An Airplane

• A bird

• A football thrown by Carson Palmer

• A “dumb” bomb

• A “smart” bomb

• A bird that has just died in mid flight

• A skydiver

Demonstration

• Two identical metal balls are launched simultaneously. One is projected horizontally; the other falls only vertically. Which ball will strike the ground first?

Two balls that start to fall at the same time.

The one on the right has an initial speed in the x-direction.

It can be seen that vertical positions of the two balls are identical at identical times…

while the horizontal position of the yellow ball increases linearly.

Slow Motion Camera

Projectile Motion

• Horizontally

–Acceleration is zero!

• Vertically

–Acceleration is due to gravity

• Time of flight is equal for horizontal and vertical movement.

Observe independent vectors

3-5 Projectile Motion

A projectile is an object moving in two dimensions under the influence of Earth's gravity; its path is a parabola.

Demonstration

• When the plunger in the dynamics car is released, the ball is launched straight up. Will the ball land in front of, in, or behind the moving dynamics cart?

It can be understood by analyzing the horizontal and vertical motions separately.

3-5 Projectile Motion

3-5 Projectile Motion

If an object is launched at an initial angle of θ0 with the horizontal, the analysis is similar except that the initial velocity has a vertical component.

Draw velocity vectors for this. Label the magnitudes

3-6 Solving Problems Involving Projectile Motion

Projectile motion is motion with constant acceleration in two dimensions, where the acceleration is g and is down.

3-6 Solving Problems Involving Projectile Motion

1. Read the problem carefully, and choose the object(s) you are going to analyze.

2. Draw a diagram.

3. Choose an origin and a coordinate system.

4. Decide on the time interval; this is the same in both directions, and includes only the time the object is moving with constant acceleration g.

5. Examine the x and y motions separately.

3-6 Solving Problems Involving Projectile Motion

6. List known and unknown quantities. Remember that vx never changes, and that vy = 0 at the highest point.

7. Plan how you will proceed. Use the appropriate equations; you may have to combine some of them.

At the 2003 World Punkin’ Chunkin’ Championships the

winning chunk was launched with an initial speed of 113 meters/sec.

At an angle of 45 degrees

• Determine: 1. The horizontal and vertical components of velocity2. The time of flight for the pumpkin (wow)3. The range of the pumpkin

3-7 Projectile Motion Is ParabolicIn order to demonstrate that projectile motion is parabolic, we need to write y as a function of x. When we do, we find that it has the form:

This is indeed the equation for a parabola.

p. 66 #17

• A tiger leaps horizontally from a 6.5 m high rock with a speed of 3.5 m/s. How far from the base of the rock will she land?

Sample on page 58 3-5

Homework Chapter 3

• Question: page 65 #15

• Problems: 18, 19, 21, 22

• Extra Practice

• Projectile Motion – Guided activity

• http://www.physicsclassroom.com/Class/vectors/U3L2a.cfm

Closure

• Kahoot (Projectile Motion)

• How does the downward components of the motion of a projectile compare with the motion of freefall?

Homework Chapter 3

• Problems: 26, 31, 35