
Objectives 
Essential Question:If Bob stands on the edge of the
Grand Canyon and throws a penny straight down or throws it horizontally why or why not would it be in
freefall? 
Forms of Freefall

Define
freefall.
In freefall gravity is the only force acting on an
object (air resistance is negligible)

Define projectile motion.
(An object in
freefall given a starting velocity.)

State the type of curve a projectile will
follow when given constant velocity in one dimension and constant
acceleration in another. (Parabola)

State the name of the path a projectile
follows. (Trajectory)

State the acceleration in the x and y dimensions
for projectile motion.
 xdimension accel = 0 always
 ydimension accel = 9.8 m/s/s downward on Earth always

State the condition of velocity in both the x and
y dimensions.
 xdimension velocity = constant
always
 ydimension velocity = variable always

State the relationship of the velocity & acceleration
vectors in the x direction to those in the y direction.
Homefun (formative/summative
assessment): Questions 1, 3, 5, 7, 9, p. 91; Problems 9, 11,
13, 17
Relevance: The understanding of objects in
freefall is a key element in many forms sports including sky diving, skate
boarding, ski jumping, etc.


Activities 
 Lesson 1
 Key Concepts: Projectile motion
as a form of freefall.
 Purpose: Model
projectile motion assuming no air resistance and constant
acceleration in the ydimension.
Interactive Discussion:
Objectives 15.
Floppy
Disk Projectile
Demo:
If the x and y dimensions are independent
then two disks projected horizontally at nearly the same time should
strike the floor at nearly the same time even if they have different
velocities. (Place a floppy on the edge of a desk and knock it off
with two floppies taped together so that all the floppies fly over
the edge almost simultaneously.)
In Class Problem Solving:
 Private Jackson drops a cannon ball when the cannon fires
Resources/Materials: 3 floppy
disks, two taped together. 

Essential Question:
If we ignore air resistance is
there any force to produce acceleration in the xdimension and what
does this tell us about xdimension velocities? 
 Projectile Motion with Various Launch Angles
 Bombs and Baseballs

Solve bomber problems.
 Why did the Japanese use a high level horizontal bomber
in WWII to sink the USS Arizona?
 Why would horizontal bombers not normally be
used against ships in naval battles?

Solve
artillery
(baseball) problems.

State the relationship between the range for projectiles
launched at complementary angles with the same initial velocity.
 Why would the Confederates use complementary angles to
bombard Fort Sumter?
Homefun (formative/summative
assessment):
Read:
Insultingly Stupid Movie Physics
 Chapter 8, Hollywood Bombs: How Filmmaker
Physics Misses the Boat, pp 117  133
Relevance: From throwing stones to
modern artillery, the understanding of projectile motion has had a
profound influence on history.


 Lesson
2
 Key Concept: The
x and y components are independent
 Purpose: Solve projectile motion problems
with various launch angles.
Video Clip:
Show a video clip of the Bombing
of USS Arizona, Pearl Harbor Video
Interactive Discussion:
Objective 8 & 9. Review minilab results.
Group Problem Solving:
Working in teams of two, calculate the ranges for angles from 10 to
80 degrees in increments of 10 degrees. List the findings in on the
white board. Plot the results and state a conclusion.
Resources/Materials: Pearl
Harbor Video 

Essential Question:
Does the force of gravity ever
flip flop and what does this tell us about the acceleration due to
gravity used in projectile motion calculations? 
 Projectile Motion with Different
 Launch and Landing Elevations

Solve projectile motion problems for various take off angles when the impact
point is above or below the launch point.
Some Movies with
Projectile motion:

Speed

True Lies

Back to the Future II
Homefun (formative/summative
assessment):
Read:
Insultingly Stupid Movie Physics
 Chapter 9, Leaping Logic: Why Moviemakers Say,
"How High" When the Director Says Jump, pp 133  147
Relevance: Projectile motion is a key
element in action movies. 

 Lesson 3
 Key Concept: Using components to take advantage
of the independence of x and y dimensions.
 Purpose: Solve projectile motion problems
with various launch angles and with starting and ending points
at different locations.
Interactive Discussion:
Objectives. Projectile motion in movieshow it's really done. Why
do jumpers need a landing ramp? Why are stunt drivers buckled into
special suspension systems?
In Class Problem Solving:
See list under objectives


Essential Question:
How has projectile motion
helped shape history? 
 Hitting Targets With Projectiles
 in the Real World

Describe the equations used to model air resistance force (F_{r}).
 Low speed: F_{r} proportional
to velocity
 High speed: F_{r} proportional
to (velocity)^{2}

Sketch the trajectory of a hypothetical projectile with and without air
resistance.

Solve projectile motion problems when the target is moving.
 Why would a WWII bomber be difficult for a ship to
shoot down?
 Why would dive bombers be more accurate than horizontal
bombers?
 What factors would have made the
the fatal shot in the
Kennedy assassination easy, assuming it was fired by Oswald?
Relevance: Projectile
motion can help shed light on whether Kennedy was or was not shot by a lone
assassin.


 Lesson 4
Key Concept: To
understand projectile motion is to gain a deeper understanding of history
including WWII, the American Civil War, the Kennedy
assassination etc.
 Purpose: Give students an
understanding of how complex projectile motion problems can
become and on the part solving them has played in history.
Interactive Discussion:
Objectives.


(formative/summative assessment)
 MiniLab
Physics Investigation (Requires only Purpose,
data, and conclusion)

Title 
Analysis
of motorcycle jump in True Lies 
Purpose 
Determine if the bad
guy could have survived the motor cycle jump without being
injured. 
Overview 
The bad
guy drives a motorcycle off the top of a sky scraper, flies
across a roadway, and lands in a swimming pool on top of a
shorter sky scraper. He is uninjured. 
Data,
Calculations 
Using your observations from the movie:
 Calculate how far the bad
guy falls by measuring the time of the fall and making
appropriate assumptions.
 Estimate the bad guy's
horizontal velocity ( assume the motor cycle's max
velocity is 0.5 g on top of the building. measure the
corresponding time and calculate final xvelocity.)
 Estimate how far the bad guy travels horizontally during
the jump. (Use objects in the movie for the scale or
multiply xvelocity times time.).
 Estimate the bad guy's total velocity on impact.
(Convert this to miles per hour.)

Questions,
Conclusions 
Is it likely that the bad guy
could have walked away uninjured?

Resources/Materials: 
True Lies Video, stop watches 

Essential Question:
What is the single biggest reason
to use a computer for modeling projectile motion problems? 
Computer Analysis of Projectile Motion
 Solve Projectile motion problems with a computer
simulation (Interactive physics)
Relevance: With
complex situations, a computer analysis is often needed to insure accurate
results. 

Lesson 5
 Key Concept: How Computers
are Used for Projectile Motion Problems
 Purpose: Introduce
students to the modeling of complex problems.
Interactive Discussion:
Objectives.
In Class Problem Solving:
See MiniLab below.


(formative/summative assessment)
 MiniLab
Physics Investigation (Requires only Purpose,
data, and conclusion)

Title 
Analysis of Bus jump in Speed 
Purpose 
Determine if the bus could have made the jump under the right
circumstances. 
Overview 
In the movie a bus is depicted
jumping a 50 ft gap in a highway overpass but there is no
incline. 
Data,
Calculations 
Use both interactive physics and pencil&
paper calculations to determine if the jump could have been
made under the right conditions without wrecking the bus
. Run the simulation both with and without air resistance. 
Questions,
Conclusions 

What assumptions in the hand calculations
would be likely to introduce significant errors.
 Does inclusion of air resistance in
the simulation significantly affect the results?

Resources/Materials: 
Speed video 

Essential Question:
Is a circular orbit a form of
freefall? 

State the direction of centripetal
acceleration and force.

Compare circular to projectile
motion.

Calculate centripetal
acceleration.
a_{c} = v^{2}
/ r
 State why
centripetal acceleration is not actually constant.
 Calculate period
(T) of an object in centripetal motion.
T = (2pr) / v_{T }
Homefun
(formative/summative assessment): Problems 25, 27, 29
Summative Assessment: Unit
Exam objectives 1 21
Relevance: An understanding of
circular motion is basic to an understanding of orbits not to
mention space movies. 

 Lesson 6
 Key Concept: Uniform
circular motion results in radial or centripetal acceleration.
 Purpose: Understand
the similarities and differences between circular and
projectile motions.
Interactive Discussion:
Objective. Define tangential velocity, centripetal acceleration
and force.
In Class Problem Solving:

Vertical circle

Horizontal circle
