```Course: Physics
I.
II:
Unit Title:
III.
Unit Length:
schedule)
IV.
Physics Unit 2
Two-Dimensional Motion
10 days (block schedule) or 18 days (traditional
Major Learning Outcomes:
This unit is focused on the concept of two dimensional motion. Students will learn about
the relationships for motion that occurs simultaneously in two dimensions. Students will
examine the horizontal and vertical components of projectile motion, including position,
velocity, and acceleration. Students will extend the study of two dimensional motion to
include uniform circular motion. Specifically students will be able to:
Projectile Motion
 Identify a frame of reference for measurement of position for projectile motion.
 Analyze and evaluate the position, velocity and acceleration in horizontal and
vertical frames of reference for projectile motion.
 Apply the concepts of position, velocity and acceleration developed in Unit One
to solve conceptual and quantitative problems for projectile motion in both
horizontal and vertical reference frames.
 Describe the path of a projectile as parabolic.
 Describe the effects of changing launch speed and launch angle on the path of a
trajectory.
 Clarify (for horizontal component of projectile motion) that velocity is constant.
vx = (vlaunch)(cos θ launch) ax = 0 m/s2 xf =xi + vt (note that θ is measured from
the x axis)
 Clarify (for vertical component of projectile motion) that velocity changes and
acceleration is that of gravity. ay = g = -9.8 m/s2 vi = (vlaunch) (sin θ launch)
vf = vi + gt
yf = yi +vit + ½ g t2
vf2= vi2+2gy (note that θ is
measured from the x axis)
Uniform Circular Motion
 Define uniform circular motion, incorporating magnitude and direction.
 Apply the concept of vectors to observe acceleration for an object traveling at
constant speed in a circular path.
 Distinguish between speed and velocity for an object in uniform circular motion.
Application of Graphical and Mathematical Tools
Projectile Motion—Horizontal Motion:
 Measure horizontal position versus time of an object moving in a trajectory.
 Sketch a position versus time graph of the projectile path for both horizontal
motion of a projectile.
 Recognize that the relationship is linear for horizontal motion.
Physics- Unit 2
DRAFT
1


Identify the slope of the line as the change in position over time (velocity) and the
y-intercept as the initial position for the given time interval. Note that the slope of
position, time for horizontal motion is constant and thus velocity is constant.
Recognize that a constant velocity means that acceleration for horizontal motion
is zero!
Projectile Motion—Vertical Motion:
 Measure vertical position versus time of an object moving in a trajectory.
 Sketch a position versus time graph of the projectile path for vertical motion of a
projectile.
 Recognize that the relationship for position versus time is parabolic for vertical
motion.
 Identify the slope of the line as the change in position over time (velocity) and the
y-intercept as the initial position for the given time interval. Note that the slope of
position, time for horizontal motion is not constant and thus velocity is not
constant.
 Recognize that a parabolic position versus time graph means that acceleration is
constant for vertical motion!
a  v
x f  xi  vit  1 at 2
t
2
2
2
where a = g
v f  vi  2ax
V.
Content Objectives Included (with RBT Tags):
COMPETENCY GOAL 1: The learner will develop abilities necessary to do and
understand scientific inquiry.
1.01 Identify questions and problems that
investigations.
(RBT B2, B3, C2, C3)
Physics- Unit 2
DRAFT
This goal and these objectives are an
integral part of each of the other goals. In
order to measure and investigate scientific
phenomena, students must be given the
opportunity to design and conduct their
own investigations in a safe laboratory.
The students should use questions and
models to formulate the relationship
identified in their investigations and then
report and share those finding with others
Students will be able to:
 Develop questions for investigation
from a given topic or problem.
2
1.02 Design and conduct scientific
the physical world.
• Create testable hypotheses.
• Identify variables.
• Use a control or comparison group when
appropriate.
• Select and use appropriate measurement
tools.
• Collect and record data.
• Organize data into charts and graphs.
• Analyze and interpret data.
• Communicate findings.
(RBT C2, C3, C4, C5, C6)
1.03 Formulate and revise scientific
explanations and models using logic and
evidence to:
• Explain observations.
• Make inferences and predictions.
• Explain the relationship between
evidence and explanation.
(RBT B2, B6, C2, C6)
1.04 Apply safety procedures in the
laboratory and in field studies:
• Recognize and avoid potential hazards.
• Safely manipulate materials and
equipment needed for scientific
investigations.
(RBT B3, C3)
3.01
Analyze and
evaluate
projectile motion
in a defined
frame of
reference.
(RBT B4, C3,
B4)
Physics- Unit 2

Distinguish and appropriately graph
dependent and independent
variables.

Discuss the best method of
graphing/presenting particular data.

Use technology resources such as
graphing calculators and computers
to analyze data.

Report and share investigation
results with others.

Use questions and models to
determine the relationships
between variables in investigations.
Use evidence from an investigation
to support a hypothesis.


Predict safety concerns for
particular experiments
o Electricity
o Projectiles
 Relate physics concepts to safety
applications such as:
o Transportation: seat belts,
air bags, speed…
Short circuits, circuit breakers, fire
hazards
Resolve vectors into vertical and horizontal components:
a
c
b
a 2  b 2  c2
sin   a
c
b
cos  
c
DRAFT
3



3.02
Design and
conduct
investigations of
two-dimensional
motion of
objects.
(RBT C6 ,D5)
3.03
Analyze and
evaluate
independence of
the vector
components of
projectile motion.







(RBT C3)



3.04
Evaluate,
measure, and
analyze circular
motion

(RBT B3 , C3)







Physics- Unit 2
tan   a
b
Evaluate the motion of a projectile both horizontally and
vertically.
Recognize that the horizontal component of velocity does not
change (neglecting air resistance).
Recognize that the vertical component of velocity does
change due to gravity at the rate of 9.8m/s2 downward.
Select appropriate measurements for an investigation of
projectile motion.
Identify factors that may affect results.
Predict and measure the path of the projectile including
horizontal range, maximum height, and time in flight (such as
a projectile launched horizontally or from the ground at a
given angle).
Recognize that vector components are independent of each
other.
Apply the equations of uniform velocity to the horizontal
component.
Apply the equations of accelerated motion to the vertical
component of velocity.
Relate height, time in air and initial vertical velocity (such as a
projectile launched horizontally or from the ground at a given
angle).
Relate range of projectile, time and initial horizontal velocity
(such as a projectile launched horizontally or from the ground
at a given angle).
Relate height and time in the air to the initial vertical velocity
Relate range of projectile to time in flight and initial horizontal
velocity
Recognize that an object may move with constant speed but
changing velocity.
Recognize that the directions of the velocity and acceleration
vectors are perpendicular to each other.
Understand that centripetal acceleration is a consequence of
the changing velocity due to change in direction.
Design and conduct investigations of circular motion.
Experimentally verify the proportional relationships described
in 3.06.
Combine proportional relationships into a single equation.
Calculate velocity using radius or circumference of the circle
and time to complete one or more cycles.
Calculate centripetal acceleration as the velocity squared
DRAFT
4
3.05
Analyze and
evaluate the
nature of
centripetal
forces.

(RBT B3, C3)

3.06
Investigate,
evaluate and
analyze the
relationship
among:
• Centripetal
force.
• Centripetal
acceleration.
• Mass.
• Velocity.


(RBT C6, D4)
Honors
(RBT C6, D4)





2
divided by the radius: ac  vr
Evaluate and understand that a net force is required to
change the direction of a velocity vector.
Understand that for uniform circular motion the net force is
called the centripetal force.
Understand that the centripetal force is not the result of
circular motion but must be provided by an interaction with an
external source.
Evaluate the direction of the force and acceleration vectors as
pointing to the center of the circle in the case of constant
speed but not constant acceleration
Design and conduct an investigation of circular motion.
Apply the proportional relationship between force and speed
Apply the inverse relationship between force and radius when
speed is constant.
Apply the formula for centripetal force as mass times
centripetal acceleration using the following equations:
2
ac  vr
2
Fc  mrv
Suggested Honors Project: Bottle Rockets
VI.
English Language Development Objectives (ELD) Included:
NC English Language Proficiency (ELP) Standard 4 (2008) for Limited English
Proficiency Students (LEP)- English Language learners communicate information,
ideas, and concepts necessary for academic success in the content area of science.
Suggestions for modified instruction and scaffolding for LEP students and/or students
who need additional support are embedded in the unit plan and/or are added at the end
of the corresponding section of the lessons. The amount of scaffolding needed will
depend on the level of English proficiency of each LEP student. Therefore, novice level
students will need more support with the language needed to understand and
demonstrate the acquisition of concepts than intermediate or advanced students.
Physics- Unit 2
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5
VII. Materials/Equipment Needed:
Most of the activities for this unit use inexpensive and simple materials. Those
materials can be found here.
Meter sticks
String
Compasses
Rulers
Blank paper
Protractors
Measuring tape
Golf balls/marbles
VIII.
Rulers with troughs (to
be used as ramps
Stopwatches
Small boxes or soup
cans
Toy dart guns
Small blocks of wood
Duct tape
Photogates and
LabPros (optional)
Soccer balls
Rubber stoppers
Small hollow tubes (6-10
cm)
Dental floss (or other
strong string)
washers
Detailed Content Description:
Please see the detailed content description for each objective in the Physics Support
of Study at:
http://www.ncpublicschools.org/curriculum/science/scos/2004/27physics
IX.
Unit Notes:
Overview of Unit Two
This unit is focused on the concept of two-dimensional motion. Students will learn about
the relationships for motion that occurs simultaneously in two dimensions. Students will
examine the horizontal and vertical components of projectile motion, including position,
velocity, and acceleration. Students will extend the study of two-dimensional motion to
include uniform circular motion.
The Unit Guide below contains the activities that are suggested to meet the Standard
Course of Study (SCOS) Goals for Unit Two. The guide includes activities, teacher
notes on how to implement the activities, and resources relating to the activities which
include language objectives for LEP (Limited English Proficient) students. Teachers
should also consult the Department of Public Instruction website for English as a
Second Language at: http://www.ncpublicschools.org/curriculum/esl/ to find additional
resources. If a teacher follows this curriculum (s)he will have addressed the goals and
objectives of the SCOS. However, teachers may want to substitute other activities that
teach the same concept. Teachers should also provide guided and independent
practice from the textbook or other resources.
Physics Support Document
Teachers should also refer to the support document for Physics at
http://www.ncpublicschools.org/curriculum/science/scos/2004/27physics for the detailed
Physics- Unit 2
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6
content description for each objective to be sure they are emphasizing the specified
concepts for each objective.
Reference Tables
The North Carolina Physics Reference Tables were developed to provide essential
information that should be used on a regular basis by students, therefore eliminating the
need for memorization. It is suggested that a copy be provided to each student on the
first day of instruction. A copy of the reference tables can be downloaded at the
following URL:
http://www.ncpublicschools.org/docs/curriculum/science/scos/2004/physics/referenceta
bles.pdf
Essential Questions for Unit Two:
Essential questions are those questions that lead to student understanding. Students
should be able to answer these questions at the end of an activity. Teachers are
advised to put these questions up in a prominent place in the classroom. The questions
can be answered in a journal format as a closure.
1.
Compare and contrast the processes of vector resolution and vector addition.
2.
How do the vertical and horizontal components of a projectile’s velocity
change?
3.
How can the trajectory of a projectile be predicted?
4.
How do linear and projectile motion relate to each other? How are they
different?
5.
How can an object moving at constant speed experience an acceleration?
6.
How do you evaluate the centripetal acceleration of an object?
7.
How is a force applied to create circular motion?
8.
How do mass, velocity, and radius relate to centripetal force?
9.
Why is centrifugal force a fictitious quantity in physics?
10.
How would you design a lab to measure the relationships between mass,
Safety
 No object should be thrown at another person at any time unless part of a lab
activity.
 Hard-toed shoes should be worn in physics labs.
 Read all instructions before starting the lab activity.
 If lab equipment appears to be malfunctioning, contact the science teacher
immediately.
 All students should be aware of what others are doing when lab activities are
taking place.
 Keep lab area as clean as possible.
Physics- Unit 2
DRAFT
7
Modified Activities for LEP Students
Those activities marked with a  have a modified version or notes designed to assist
teachers in supporting students who are English language learners. Teachers should
also consult the Department of Public Instruction website for English as a Second
Language at: http://www.ncpublicschools.org/curriculum/esl/ to find additional
resources.
Computer Based Activities
Several of the recommended activities are computer based and require students to visit
various internet sites and view animations of various biological processes. These
animations require various players and plug-ins which may or may not already be
essential for the teacher to try them on the computers that the students will use and to
consult with the technology or media specialist if there are issues. These animations
also have sound. Teachers may wish to provide headphones if possible.
Web Resources
Please keep in mind that as individuals make changes to websites, it is possible that the
websites may become inactive. These resources are provided to supplement the
activities in the unit. Some of the resources can be used as to supplement your teacherled discussions by projecting them for the class. Other activities require students to
Support for all students from Physics
(Giancoli) on vectors and two
dimensional motion.
http://lectureonline.cl.msu.edu/~mmp/kap3/cd This applet simulates projectile motion.
060.htm
To fire the cannon, click or drag in the
black area to establish the angle of the
shot, or type an angle in the angle field.
Next, choose a muzzle velocity for the
shot. The data of each of your shots will
be stored for later reference.
http://www.cabrillo.edu/~dbrown/tracker/
Tracker is a free video analysis software
digital video. One example is Ball Toss
which tracks a tossed ball with a point
mass.
http://cwx.prenhall.com/giancoli/chapter3/del
uxe.html
Physics- Unit 2
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8
http://www.forgefx.com/casestudies/prenticeh This interactive 3D simulation allows
all/ph/catapult/catapult.htm
students to work on the development of
a virtual catapult, capable of launching
giant paintballs. Using the Design and
Test methodology, students must create
their catapult so that it is capable of
distance, height, and strength.
http://hippocampus.org/Physics
A wonderful site with video
presentations, labs, and other
materials—all free and all of great
quality.
http://www.vjc.moe.edu.sg/fasttrack/physics/ Animations for both circular motion and
projectile motion.
rotational motion. Rotate the merry-goround to change its angle, or choose a
constant angular velocity or angular
acceleration. Explore how circular
motion relates to the bug's (x,y) position,
velocity, and acceleration using vectors
or graphs.
http://physics.doane.edu/physicsvideolibrary/ These basketball clips show a basic free
default.html#projectile
throw type shot. They are intended to
show projectile motion. Also included is
a soccer kick from the back of a truck
and video of a shuttlecock
Physics- Unit 2
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9
http://www.saintmarys.edu/~rtarara/LAB.html
These are separate modules in a new
series of laboratory simulations
designed to serve as both pre and post
lab tools. Typical data can be generated
and analyzed. FREEFALL: This
simulation uses the Pasco time of flight
apparatus to time vertically falling balls-a small golf ball or a large, light, plastic
ball. Timing is done with the Pasco
smart timer. This experiment is
designed to familiarize students with the
concepts of acceleration by having them
plot height versus time data.
CENTRIPETAL FORCE: Based on the
most common equipment setup, this
animation follows the basic
experimental procedures for
determining the rotational parameters
for measuring centripetal force. This
animation is more of a 'cartoon' than
most of the others (rotational animations
are difficult) but the apparatus is
reasonably well created.
sci/phys/Class/vectors/vectoc.html
http://wps.prenhall.com/esm_walker_physics
_2/0,7966,802031-,00.html
http://id.mind.net/~zona/mstm/physics/mecha
nics/vectors/introduction/introductionVectors.
html
This site offers excellent background
material on vectors and projectiles.
Vector chapter presentation offers good
background for teachers and students.
Good introduction to vectors offers a
great overview.
X.
Global Content: Aligned with 21st Skills:
One of the goals of the unit plans is to provide strategies that will enable educators to
develop the 21st Century skills for their students. As much as students need to master
the NCSOS goals and objectives, they need to master the skills that develop problem
solving strategies, as well as the creativity and innovative thinking skills that have
become critical in today’s increasingly interconnected workforce and society. The
the skills and resources related to the 21st Century classroom.
mid=120
Physics- Unit 2
DRAFT
10
NC SCS
Physics
21st Century Skills
Communication Skills
Goal 1, 3.01-3.06 Conveying thought or opinions
effectively
Goal 1, 3.01-3.06 When presenting information,
distinguishing between relevant
and irrelevant information
Goals 1-8, 3.04 Explaining a concept to others
Interviewing others or being
interviewed
Computer Knowledge
Goals 1-8, esp. Using word-processing and
Goal 1, 3.04 &
database programs
3.05
Goals 1-8, esp. Developing visual aides for
Goal 1, 3.02 &
presentations
3.05
Goal 1, 3.02
Using a computer for
communication
3.02
Learning new software programs
Goals 1-8, 3.033.05
Goals 1-8, esp.
Goal 1, 2.04,
3.02, 3.05, 4.07,
6.04, 7.01, Goal
8, 3.03
Goals 1-8, 3.01
Employability Skills
Assuming responsibility for own
learning
Persisting until job is completed
Working independently
Developing career interest/goals
Goal 1, 3.01,
Responding to criticism or
3.02, 3.04, 3.06 questions
Information-retrieval Skills
Goal 1. 3.01-3.03 Searching for information via the
computer
Goal 1
Goals 1-8, 3.013.06
Physics- Unit 2
Searching for print information
Searching for information using
community members
Following written directions
DRAFT
Activity


Questions in all
Laboratory Activities
Data collection in all Lab
Activities

Projectiles at an Angle

Circular Motion

Circular Motion


Investigation of Projectile
Motion
Investigation of Projectile
Motion

Circular Motion

Exploring Projectiles

Vector Treasure Hunt

Questions in all Lab
Activities

Investigation of Projectile
Motion
Most of the activities can be
presented as opportunities for
11
Goals 1-8, 3.013.06
Goals 1-8, 3.03
Goal 1, 3.03
Goals 1-8
Identifying cause and effect
relationships
Summarizing main points after
Locating and choosing
appropriate reference materials
Language Skill - Writing
Using language accurately
Organizing and relating ideas
when writing
Proofing and Editing
Goals 1-8
Goals 1-8, 3.013.06
Goals 1-8, esp.
Goal 1, 3.01-3.06
Goals 1-8, esp. Synthesizing information from
Goal 1, 3.01-3.06 several sources
Goal 1
Documenting sources
Developing an outline
1.04, 3.01-3.06 Writing to persuade or justify a
position
Creating memos, letters, other
forms of correspondence
Teamwork
Goal 1, 2.04,
Taking initiative
3.02, 3.06, 4.06,
6.01, 6.04, 7.01,
8.02, 8.03, 8.04
Goal 1, 2.04,
Working on a team
3.02, 3.06, 4.06,
6.01, 6.04, 7.01,
8.02, 8.03, 8.04
Thinking/Problem-Solving
Skills
Goals 1-8, 3.01- Identifying key problems or
3.06
questions
Goals 1-8, 3.01- Evaluating results
3.06
Goals 1-8
problems
1.01, 2.04, 3.02, Developing an action plan or
3.06, 4.06, 6.01, timeline
6.04, 7.01, 8.02-
Physics- Unit 2
DRAFT
directions. The teacher will
have to work with most students
to develop this skill over time.
 “Explain” and “Evaluate”
in all lab activities
 Exploring Projectiles

Investigation of Projectile
Motion

“Explain” and “Evaluate”
in all lab activities
“Evaluate” in all lab
activities
“Explain” and “Evaluate”
in all lab activities



“Evaluate” in all lab
activities

All Lab Activities

All Lab Activities

All Lab Activities

All Lab Activities
12
04
Physics- Unit 2
DRAFT
13
Teacher’s Guide- Vector Treasure Hunt
This activity is designed to help students understand the graphical method of vector
addition, and to understand the idea that the order in which the vectors are added has
no effect on the final outcome. Day One of the activity should be done after the
graphical method has been introduced, but before the algebraic component
(mathematical) method has been introduced. Day Two of this activity should either be
done after the algebraic method is introduced, or question #1 from the post lab should
be omitted.
Language (ELP) Objectives for LEP Students:
 Print a copy of MapQuest directions from school to a familiar destination
and make an overhead as a demo.
 After students have completed the graphical directions of their map, have
them write out the specific directions from the initial to the final destination.
Engage
Introduce this activity by telling the students that they will be participating in a treasure
hunt, but that there is a trick…they have to create the directions for another group to
follow. Utilizing a treasure hunt increases student interest in vectors.
Explore
Students are asked to work together to create a series of directions for other students to
follow. Students should be encouraged to be creative with the directions to keep things
interesting. As the students are working on their directions, the teacher should circulate
to ensure that they are writing clear, concise directions. Before the students complete
the second part of the activity, it is also recommended that the teacher provide some
kind of “treasure” to be found at each landmark (ending point).
Explain
The development of the “maps” (graphical addition of the vectors) gives students the
opportunity to practice the graphical method. The shuffling of the cards raises the
question of whether or not the order of the vectors matters and allows an opportunity for
the students to prove to themselves that the outcome is not affected. This is one
reason why it is recommended that there is an actual “treasure” at the end. Finding the
treasure is proof to the students that the order did not matter.
Key to pre- and post-lab questions
Remember, pre-lab questions are designed to get students to start thinking about the
concepts involved in the activity. Students should not always be expected to know the
correct answers to the pre-lab questions.
1. A vector must have a magnitude and a direction.
2. Student answers will vary, but most will think that the order does matter.
Physics- Unit 2
DRAFT
14
1. There are far too many vectors to resolve each into components and then add
them to find the resultant.
2. After completing the activity, students should recognize that the order of the
directions did not matter because their resultant displacement was the same as
the group that created the directions.
Physics- Unit 2
DRAFT
15
Vector Treasure Hunt
Objectives
 Use appropriate measurements (distances and angles) to provide a list of written
directions
 Interpret the directions written by a different group
 Use graphical addition to create a map of the other group’s directions
Pre-Lab Questions
1. In order to have a vector quantity, which two types of data must be obtained?
2. Do you think that the order in which vectors are added makes a difference in the
final outcome? Why or why not?
Materials






Compass
Ruler
Protractor
Meter stick or measuring tape
Paper and pencil
Blank paper
Physics- Unit 2
DRAFT
16
Lab Instructions – Day One
1.
To complete this activity in a timely manner, you will need to convert between
meters and number of footsteps. Choose one person in your lab group to be
the “walker”, and have them practice walking so that they move exactly one
meter. Suggestion: walk heel to toe and count how many “feet” are in a
meter.
2.
After your walker has mastered this, choose a starting point, and record that.
You should be very specific. Tell the other group where to start, and what
they should see at that point. Then you may begin working on your set of
directions. You should have at least 15 individual vectors, but no more than
20. Each direction should be written on a separate index card. You may
include some fun, silly directions, but the important part is the part that will be
mapped: the vectors. Your final direction should have them stopping at some
recognizable campus landmark, but DO NOT write the name of the landmark
in the directions.
3.
After you have completed your list, use the graphical method of vector
addition to make a map of your directions. You should clearly label the
resultant displacement on the map, and record the landmark they should be
facing at the end. Record the magnitude and direction of the resultant
displacement on the bottom of the page.
Lab Instructions – Day Two
1.
Obtain a set of instructions from another group, and find their starting point.
You should now proceed to follow their directions until you get to the end.
Make a note of any directions that are unclear.
2.
Using the graphical method of vector addition, make a map of the directions
you just walked. Be sure to find the magnitude and direction of your resultant
displacement. Record the name of the landmark that you find at the end.
Post-lab Questions
1.
Why might it be inappropriate to use the algebraic component (mathematical)
method of vector addition for this activity?
2.
The sets of index cards containing the directions were shuffled before they
were passed out. Did the order of the directions make any difference in the
final outcome? Why or why not?
Physics- Unit 2
DRAFT
17
Physics- Unit 2
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18
Physics- Unit 2
DRAFT
19
Physics- Unit 2
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20
Teacher Guide: Exploring Projectiles
Notes to Teacher:
 This activity should be done after students have a good grasp of both graphical
and algebraic methods of vector addition
 Students are taken outside, where they are told to design a method to determine
the distance between two points which are separated by a large obstacle, such
as a building
 Class time can be saved by introducing the activity and showing the students the
two points on one day, and having them design their procedure for homework.
Then they can complete the lab on a different day.
Language (ELP) Objectives for LEP Students:
 Define key terms; magnitude, direction, and vector.
 Describe verbally or in paragraph form the relationship between these terms
and provide an example.
ENGAGE:
In the pre-lab discussion, ask students to raise their hand if they play a sport of some
type. Then ask them to raise their hand if they play a sport that involves a projectile.
This is an excellent time to define a projectile as any object that travels through the air
and accelerates only under the force of gravity. Only a few sports such as Track and
Field, curling, and biking do not incorporate a projectile at some point.
EXPLORE:
This experiment is designed to emphasize to the student the effect of increased speed
on the distance the projectile travels horizontally. Another important emphasis is that the
time in the air is independent of the initial speed if the projectile leaves the table at an
angle of zero degrees with the horizontal. Check to make sure all groups have the
launch device away from the edge of the table so that the projectile leaves the table
horizontally.
If computers are available students may use an online stopwatch program from
Clemson University
http://phoenix.phys.clemson.edu/labs/stopwatch.html
OR
they may use a program that may be loaded into their calculator
http://www.ticalc.org/pub/83plus/basic/programs/
EXPLAIN:
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ELABORATE:
The last question asks students to elaborate.
EVALUATE:
The Challenge part of the experiment allows students to evaluate how well they took
data.
1) The greater the angle of the ramp, the larger the value of distance 2 measures.
2) Possible answers are height of the table, mass of the ball, length of the ruler.
3) The times should not be very different. The initial speed is all in the x direction and
as such does not affect the way the object falls. The only affect of increasing the speed
is to increase the horizontal distance that the ball travels before hitting the floor.
4) The height of the table affects the time the ball is in the air and that does not change.
For the “Challenge”, deduct only a small number of points from the grade if the target is
missed. Timing with a stopwatch is difficult.
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EXPLORING PROJECTILES
NAME:
What affects the path of a projectile? The motion of a projectile is more complicated
as it may have both horizontal motion and vertical motion. We are going to explore the
falling object by making several measurements.
You will need the following: a golf ball or marble, a ruler that has a trough or track
down the middle (most wooden and some plastics ones have this), a stopwatch, a
meterstick and a box or empty soup can.
Develop a plan. On your lab table, place the ruler about 10 cm from the edge. Find a
way to elevate the end of the ruler that is the farthest away from the end of the table.
Also find a way to change the height from which you release the golf ball or marble so
that you are not pushing it.
Distance
1(height)
Distance 2
Delegate your roles: One person should release the ball carefully and consistently.
Another should measure the height of the table and distance 2 carefully and
consistently. The hardest role is using the stopwatch to time from the instant the ball
leaves the edge of the table until it hits the floor. The last person must carefully record
the data in a neat and accurate manner. That person must create a table in which to
record data.
What Should I Measure? Please measure height of ball above table before it is
released. Measure the height of the table and the distance the ball travels horizontally
(distance 2). Measure the time the ball is in the air from table to floor.
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DATA: Place your Chart here. Label the columns as you feel appropriate.
TRIAL
1
2
3
4
5
What did we discover?
1) Does the height of the release ramp affect the horizontal distance (distance 2)?
2) Name two constants in the setup of your experiment.
3) Are the times the projectile was in the air very different for each trial? Why or why
not?
4) What affects the time the ball was in the air if it always rolls straight off the table?
CHALLENGE:
When you have completed your measurements and recorded them in the chart, your
teacher will present your group with a challenge. Your teacher will pick one of your
heights and place a box or can at the horizontal position you measured. You must hit
the object at the position the teacher selects. You shall loose ______ points every time
you must repeat the roll. Good Luck!
Teacher Notes: Deduction of ______________ points
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TEACHER GUIDE FOR Projectiles at an Angle
Notes to Teacher:
 This activity is an introductory activity for projectile motion. It helps students
visualize the connection between constant horizontal motion and accelerating
vertical motion.
 The students roll golf balls down a ramp (wooden ruler) changing the height of
the ruler. The ball leaves the ruler and rolls across the table until it rolls off the
edge. Students record the time in the air for various angles of the ruler.
Language (ELP) Objectives for LEP Students:
 Think-pair –share with another student or the whole class the procedure
for the projectile launching activity.
 Write a summary of activity and how this relates to this unit on vectors.
ENGAGE
Start the lesson by tossing a tennis ball to different students in the class. Vary the angle
of launch and try to gently throw the ball at about the same speed. Changing the angle
of launching the dart presents real challenges in making predictions for some students.
Some sample questions which may help are included below.
(1) What angle do you predict will produce the greatest horizontal distance?
(2) Does the angle affect the speed of the dart?
(3) Does the angle affect the time in the air?
(4) Why does a baseball/softball coach caution against “side-arming” a baseball?
EXPLORE
One of the most difficult parts of the lab is to measure the speed of the dart as it leaves
the dart gun.
Students must also find a stable method of creating the correct angles. Walk around the
classroom and interact with the students as they explore possible methods. One way to
do this is to ask “what is the advantage of using an ‘object’s name’ at the end of your
block?
EXPLAIN
Students will answer the questions at the end of the lab.
Evaluate
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Ask students to compare their answers with each other before turning in their labs.
Suggestions:
1) Buy dart guns at a dollar store.
2) Pencils, books, doorstops (wedges), etc can be used to elevate one end of the block.
3) An easy way to measure the speed of the dart is to shoot the dart horizontally from a
two meter height. Stand on a chair or stairway. Measure height of launch and also the
horizontal distance the dart travels. An example is provided;
Example:
x= 8 = vot and -8 = 0t – 0.5 (9.8) t2
Using the second equation, solve for t: t= 1.26. Substitute into the first equation to find
Vo. Vo = 7.6 m/s. This is a powerful dart gun!
Height=
2m
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Range=8 m
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Projectiles at an Angle
Name
The Big Question: How does the angle of launching a projectile affect where it lands?
Equipment: a dart gun with a dart, two blocks of wood of the same height, masking
tape, ruler or meter stick, protractor, duct tape, stop watch, photogates (optional)
Set-up: Tape the gun flat to the top of
one block using duct tape. The trigger
should be free of the tape. Mark the
position of the projectile block. Load the
dart into the gun.
1. Find a way to measure the speed of your dart.
2. Place an object of your choice under the right end of the projectile block so that the
following angles are created with the table: 20°, 30°, 45°, 60° and 70°.
3. Predict how far away from the right end of the projectile block the target block must
be placed so that the dart will hit it in the middle of the block.
4. Hit the target block in the middle of the block.
DATA:
Show calculations below for your speed:
Show calculations in the space below for predicted range.
For 20°
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For 30°
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For 45°
For 60°
And for 70°
Angle of
Launch (in
degrees)
Predicted
horizontal
distance (m)
(Also called
Range)
Actual horizontal
distance (m)
Number of tries to hit the
middle
20°
30°
45°
60°
70°
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Record your observations below about the process. What did you discover? Give at
least two observations relating to the physics of the experiment.
How does the angle of launching a projectile affect where it lands?
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Teacher’s Guide- How fast can you kick?
This activity is designed to be used towards the end of the study of projectiles
launched at an angle. To be able to complete the calculations, students will need to
have a good understanding of how to solve problems where they are given the initial
velocity and are asked to calculate quantities such as maximum height, time in the
air, and horizontal displacement. This lab is structured so that they do the exact
opposite process. They will start with two pieces of data; the horizontal distance
traveled and the total time in the air, and use that information to work backwards and
find the ball’s total initial velocity.
Engage: This activity engages students by asking them to figure out the speed at
which they can kick a ball. Setting up a friendly competition within the class can help
to pique student interest in the activity. Because this activity uses the reverse
process of the typical projectile motion problem, it provides an opportunity to really
gauge student understanding of projectiles.
Explore: Requiring students to develop their own procedure allows an opportunity
for them to collaborate with each other and to really think about the types of data to
collect.
Explain: During the process of designing a procedure, group members will be
required to express and evaluate their own ideas. Often group members will
disagree about the types of data to collect or about the process needed to collect
that data. These conflicts force them to discuss ideas and provide an opportunity for
them to clarify misconceptions for each other.
Elaborate: This activity requires students to link the concepts of projectile motion
that they have learned to a real problem, and to use those concepts to develop an
Evaluate: The process of designing an experiment allows students to demonstrate
their understanding of projectiles, as well as to apply that knowledge to solve a
problem.
Pre-lab
1. time, horizontal distance, some students will say they need the angle
2. Many students will say that they do need the angle, even though they don’t
because it can be calculated at the end. Often, as they are doing their final
calculations they will realize that they never need that value.
4. human error with the timer, wind and other external factors
Post Lab
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1.
a. if the angle is increased, the vertical speed increases, and the horizontal
speed decreases
b. because total time in the air only depends on the initial vertical velocity
and acceleration due to gravity, as the angle increases, time in the air
increases
c. because vertical displacement only depends on the initial vertical velocity
and acceleration due to gravity, balls kicked at a high angle will have a
higher maximum height than those kicked at a low angle
d. because the horizontal displacement depends on both the horizontal
component of velocity and the total time in the air, a simple relationship
does not exist.
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How fast can you kick?
Projectile Lab
Objectives:
 design an efficient, accurate experiment
 collect, record, and analyze data
 choose and apply appropriate equations
 apply the concepts learned in class to determine the initial velocity and maximum
height of a soccer ball
Pre-lab questions
1.
What types of data will you need to collect?
2.
What equipment will you need to complete this activity?
3.
Do you need to measure the angle at which the ball is kicked? Why or why
not?
4.
Briefly outline the methods you intend to use to complete this experiment.
5.
What are some possible sources of error in this experiment? What can be
done to reduce error?
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Data
Trial One
Trial Two
Trial Three
Calculations
For each trial, find the following: horizontal speed, maximum height, initial vertical
speed, total initial velocity (including the angle of the kick).
Trial One
Trial Two
Trial Three
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Post-Lab Questions
1.
Explain how the angle at which the ball was kicked affected each of the
following:
a. Horizontal and vertical speeds
b. Time in the air
c. Maximum height
d. Horizontal displacement
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Teacher Guide: An Investigation of Projectile Motion
ENGAGE:
The activity starts with “What do you think?” to make students think about what they
EXPLORE:
Students explore angles of launch, mass and shape, and initial velocity.
EXPLAIN:
Each exploration is followed by a request to explain what is seen and discovered
ELABORATE:
Students should share their findings after this activity in a class post-lab discussion with
the teacher.
EVALUTE:
In the post-lab discussion, evaluate the findings discussed. Make a list from the
student’s comments and clear up any misconceptions.
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An Investigation of Projectile Motion
Introduction
In this activity, you will use a computer simulation to investigate the variables of
projectile motion.
This activity is to:
Investigate the launch angle, initial velocity, and size & shape of a projectile in order
to explain how these variables affect the projectile’s motion.
Materials


Computer
Background
a) What do you think? Think about a ball flying through the air. There are many
possible things that affect the trajectory (path) of the projectile. The most
important of these factors are the angle, the initial velocity, and the size & shape
of the object being fired. Think about each variable and describe how it may
affect a projectile in motion with or without air resistance.
b) Now Experiment and Observe. Go to the PHET website
http://phet.colorado.edu, click on “Simulations,” scroll down, and select the
“Projectile Motion” simulation. You will investigate how the three variables from
part a) affect projectile motion. You want to focus particularly on the maximum
height and maximum range of the projectile.
Air Resistance should not be checked.
1. How does the angle affect projectile motion? Change the angle option to read 20o
and then click fire, and observe the resulting motion path. When it finishes, repeat the
instructions, but use angles of 30o, 45o, 60o, 70o. Compare the motion paths of each
angle, and write your observations below.
For 20:
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For 30:
For 45:
For 60:
For 70:
2. How does initial velocity affect projectile motion? Reset to DEFAULT conditions
specified above and click the “Erase” button (this should erase all your motion paths
from above). Now change the initial velocity to 15 m/s and click fire, and observe the
path. When it finishes, repeat the instructions, but use 20 m/s, 25 m/s, 30 m/s, 35 m/s,
and 40 m/s. Determine any pattern, and write your observations below.
3. Will size and shape of the projectile affect the path? If so, then how? Reset the
parameters to DEFAULT conditions and click on the “Erase” button. Change only the
objects in the trajectory and observe the pattern
4. How does size & shape affect projectile motion if there is air resistance? Reset the
parameters to default and click on the “Erase” button. Now repeat part 3, but check the
air resistance box. Observe the motion paths and record your observations below.
What affects the path?
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Teacher Guide- Circular Motion at Constant Speed
Language (ELP) Objectives for LEP Students:
 Write out a procedure for investigating the factors that affect centripetal
force
o verbally share their procedure with partner/class
o listen to verbal presentations from partner/class and write a
summary comparing and contrasting varying procedures.
ENGAGE:
If you are up to the demonstration of swinging a cup of water in a vertical circle to
illustrate the nature of centripetal force then this is a good place to do so right before the
lab. Take a strong plastic cup (clear if possible) and tie a strong string on it as shown
below. Ask students to draw a diagram of the circle and the forces acting on the cup.
Demonstrate the use of the apparatus and emphasize that they must not hold onto the
string. The washers at the end of the string must provide the only tension along the
string. (Use a large paper clip to hook the washers to the string)
EXPLORE:
Students may require your help in selecting variables. As the teacher, you may wish to
ask them before the lab to help you create a list of possible variables that will affect the
number of washers (the centripetal force) needed to keep the speed constant and
maintain a constant radius for a single trial. They should suggest mass at the end of the
string (rubber stoppers of varying mass) and radius of the path.
EXPLAIN:
Students are asked to explain their choices for the variables to investigate.
ELABORATE:
The question “What did you conclude about your data?” should force students to
examine how consistent and informative their data is. They should notice a trend—
increases, decreases or keeps the same—in the affect on centripetal force.
ELABORATE:
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“What was the relationship between the variables that you selected?” asks for a
conclusion from each student about the results they obtained.
EVALUATE:
The statement “Create a graph of your two variables to verify your statement” requires a
graphical comparison/evaluation of data.
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Circular Motion at Constant Speed
NAME:
When an object travels in a circular path at constant speed, the force is always
directed toward the center of that path. Such a force is designated as a
“CENTRIPETAL FORCE” which translates as “center seeking” force.
What affects the path of an object in circular orbit? Forces that change direction
but do not change speed always act perpendicular to the path of the object and toward
the center of the circular path that is created. We are going to explore some of the
variables for objects in circular orbits at constant speed.
You will need the following: 1 or more (up to 4) rubber stoppers of the same size, a
tube (the casing of an ink pen with both ends removed is a possibility) of 6-10 cm in
length, 2 meters of dental floss or other small, strong string, 20 washers or masses of
50 g, 100 g, 200 g, etc. masses, meter stick, and a stopwatch.
rubber
stopper
tube
washers
Procedure:
Develop a plan.
You should investigate one factor that affects the centripetal force of the object moving
in a circular path. Whether you select mass, velocity, or radius, it must be clear that all
other variables should be constant.
Which of the variables do you think should be the easiest to keep the same (so that they
become constants)?
How do you propose to maintain these variables as constants?
What did you choose to investigate? Force as a change in _____________________?
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Create a Data Chart:
TRIAL
1
2
3
4
5
What was the relationship between the variables that you selected? Create a
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EVALUATION:
Summative Evaluation:
On the following page are sample test items obtained from the WIZARD test bank
developed by eduware™ that can be used to allow students to assess their
understanding and abilities and allow the teacher to evaluate the students
understanding of key concepts and skill development for this unit.
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```