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
x f  xi  vxit
• Y- Component
1 2
gt
2
 2 gy
y f  y i  v yi t 
v yf  v yi
2
2
v yf  v yi  gt
• Vectors
v xi  vi cos( )
v yi  vi sin( )
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 horizontal
Calculate the horizontal and vertical
components of the initial velocity
After 2.0 seconds, how far has the object
traveled in the horizontal direction?
How high is the object at this point?
Solution
• Part a
 s cos30   87 m s
 v sin   100m sin 30   50 m
s
s
vix  vi cos  100m
viy
• Part b
0
0
i
x
vix 
t

x  v x t  87 m
• Part c
y  viy t 
s
2.0s   174m
  



1
1
2
g t 2  50 m 2.0s   9.8 m 2 2.0s 
s
s
2
2
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