What is Projectile Motion?

Instructional Objectives:

• Students will be able to:– Define Projectile Motion– Distinguish between the different types of

projectile motion– Apply the concept to flying marble and

measure its velocity– TEKS 5.A and 5.B

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

Examples of Projectile Motion

• Launching a Cannon ball

Variables

Horizontal Vertical

Displacement a.k.a. distance

x (xf – xi) y (yf – yi)

Initial Velocity Vxi Vyi

Average Velocity Va Va

Final Velocity  = Vxi Vyf

Time t t

Acceleration a g = 9.8 m/s2

Angle θ θ

Equations

• X- Component

• Y- Component

• Vectors

tvxx xiif

gtvv

ygvv

gttvyy

yiyf

yiyf

yiif

2

2

1

22

2

)sin(

)cos(

iyi

ixi

vv

vv

Note: g = 9.8 m/s2

(Acceleration due to gravity)

Factors Affecting Projectile Motion

• What two factors would affect projectile motion?

• Initial velocity

• Angle

Initial Velocity

Angle

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.

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.

Group Practice

• Interactive projectile motion calculator

http://library.thinkquest.org/10796/ch6/ch6.htm

• Other explanations and practice problems

http://tuhsphysics.ttsd.k12.or.us/Tutorial/Lessons/Projectile.htm#GenStrat

Class Exercise

An object is fired from the ground at 100 meters per second at an angle of 30 degrees with the horizontalCalculate the horizontal and vertical

components of the initial velocityAfter 2.0 seconds, how far has the object

traveled in the horizontal direction?How high is the object at this point?

Solution

• Part a

• Part b

• Part c

mssmtvx

t

xv

x

ix

1740.287

s

ms

mvv

sm

smvv

iiy

iix

5030sin100sin

8730cos100cos

0

0

222 0.28.9

2

10.250

2

1s

smss

mtgtvy iy

Additional Group Exercises

• See handouts, other presentations, or textbook examples

Applications

Any Ideas?

Summary of Concepts

• A projectile is any object upon which the only force is gravity,– For our purposes we will not consideration air resistance, so we will take the approach

all bodies fall at the same rate regardless of their mass

• Projectiles travel with a parabolic trajectory due to the influence of gravity,

• There are no horizontal forces acting upon projectiles and thus no horizontal acceleration,

• The horizontal velocity of a projectile is constant (a never changing in value),

• There is a vertical acceleration caused by gravity; its value is 9.8 m/s/s, down,

• The vertical velocity of a projectile changes by 9.8 m/s each second,• The horizontal motion of a projectile is independent of its vertical motion.

Independent Practice – problem sets

Set 1

Set 2

Set 3

Labs

• CPO Manual

B-1: Launch Angle vs. Range

B-2: Launch Angle vs. Speed

B-3: Analysis of Range and Speed

Acknowledgements

• gk12.poly.edu/.../RAISE...PowerPointFiles/Projectile%20Motion.ppt