colorado/physics/phys1110/phys1110_fa07/mainPage3.html

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Projectile MotionProjectile MotionPresenter: Nate MohanlallPresenter: Nate Mohanlall

2222ndnd July 2010 July 2010Mentor: Sean HendersonMentor: Sean Henderson

Concept PresentationConcept Presentation

OverviewOverview

Curriculum Placement/ExpectationsCurriculum Placement/Expectations Lesson Sequence/Teaching IdeasLesson Sequence/Teaching Ideas Projectile Motion Misconceptions / ConceptsProjectile Motion Misconceptions / Concepts Strategies for solving problemsStrategies for solving problems Applications and Societal ImplicationsApplications and Societal Implications Assessment and EvaluationAssessment and Evaluation

Curriculum Placement: BIG IDEASCurriculum Placement: BIG IDEAS

Grade 2 : Structures Grade 2 : Structures investigate and describe different kinds of movement investigate and describe different kinds of movement (e.g., by observing how toys and(e.g., by observing how toys and

other everyday objects move)other everyday objects move) identify ways in which the position of an object can be changed identify ways in which the position of an object can be changed (e.g., by pushing, by(e.g., by pushing, by

pulling, by dropping)pulling, by dropping)Grade 11 Physics: KinematicsGrade 11 Physics: Kinematics Motion involves a change in the position of an object over time.Motion involves a change in the position of an object over time. Motion can be described using mathematical relationships.Motion can be described using mathematical relationships. Many technologies that apply concepts related to kinematics have societal and Many technologies that apply concepts related to kinematics have societal and

environmental implications.environmental implications.

Grade 12 Physics: DynamicsGrade 12 Physics: Dynamics Forces affect motion in predictable and quantifiable ways.Forces affect motion in predictable and quantifiable ways. Forces acting on an object will determine the motion of that object.Forces acting on an object will determine the motion of that object. Many technologies that utilize the principles of dynamics have societal and Many technologies that utilize the principles of dynamics have societal and

environmental implicationsenvironmental implications..

A1. Scientific Investigation SkillsA1. Scientific Investigation Skills

A1.5 conduct inquiries, controlling relevant variables, A1.5 conduct inquiries, controlling relevant variables, adapting or extending procedures as required, and adapting or extending procedures as required, and using appropriate materials and equipment safely, using appropriate materials and equipment safely, accurately, and effectively, to collect observations and accurately, and effectively, to collect observations and datadata

A1.10 draw conclusions based on inquiry results and A1.10 draw conclusions based on inquiry results and research findings, and justify their conclusions with research findings, and justify their conclusions with reference to scientific knowledgereference to scientific knowledge

A1.12 use appropriate numeric (e.g., SI and imperial A1.12 use appropriate numeric (e.g., SI and imperial units), symbolic, and graphic modesunits), symbolic, and graphic modes

of representation (e.g., vector diagrams, free-body of representation (e.g., vector diagrams, free-body diagrams, vector components, and Algebraic diagrams, vector components, and Algebraic equations)equations)

B2. Developing Skills of Investigation and CommunicationB2. Developing Skills of Investigation and Communication

B2.1 use appropriate terminology related to dynamics, B2.1 use appropriate terminology related to dynamics, including, but not limited to: including, but not limited to: inertial and non-inertial frames inertial and non-inertial frames of reference, components, centripetal, period, frequency, of reference, components, centripetal, period, frequency, static friction, static friction, and and kinetic friction kinetic friction [C][C]

B2.2 solve problems related to motion, including projectile B2.2 solve problems related to motion, including projectile and relative motion, by adding and subtracting two-and relative motion, by adding and subtracting two-dimensional vector quantities, using vector diagrams, vector dimensional vector quantities, using vector diagrams, vector components, and algebraic methods [PR, AI, C]components, and algebraic methods [PR, AI, C]

C1. Relating Science to Technology, Society, and the EnvironmentC1. Relating Science to Technology, Society, and the Environment

B1.1 analyse a technological device that applies the B1.1 analyse a technological device that applies the principles of linear or circular motion (e.g., a principles of linear or circular motion (e.g., a slingshot, a rocket launcher, a race car, a slingshot, a rocket launcher, a race car, a trebuchet) [AI, C]trebuchet) [AI, C]

B1.2 assess the impact on society and the B1.2 assess the impact on society and the environment of technological devices that use environment of technological devices that use linear or circular motion (e.g., projectile weapons, linear or circular motion (e.g., projectile weapons, centrifuges, elevators) [AI, C]centrifuges, elevators) [AI, C]

Lesson SequenceLesson SequenceDay 1Day 1

Description of ActivityDescription of Activity Teaching/Learning Teaching/Learning StrategiesStrategies

Expectations Expectations AddressedAddressed

Learning Learning

StylesStyles AssessmentAssessment

Day 1:Day 1:-Diagnostic lab-Diagnostic lab:Projectile motion:Projectile motion-Vocabulary :-Vocabulary :CompleteCompletegraphic organizergraphic organizerUsing textbook Using textbook

-Group work-Independent work:Complete GraphicOrganizer-Demo ProjectileMotion (to reinforce concept quiz)

A1.5A1.10A1.12B1.1B2.1

Kinesthetic/Kinesthetic/TactileTactile

VisualVisual

LinguisticLinguistic

Diagnostic -observe students as they complete graphic organizer and perform lab -Concept quiz

Class ActivityClass Activity

http://media.ehs.uen.org/html/PhysicsQ2/Horizontal_Projectiles_03/ramp.jpg

What type of motion is the marble experiencing vertically? What type of motion is the marble experiencing horizontally?

Graphic OrganizerGraphic OrganizerKey TermsKey Terms Definition/ExplanationDefinition/Explanation

Horizontal VelocityHorizontal Velocity

Vertical VelocityVertical Velocity

Range/Max. Horizontal RangeRange/Max. Horizontal Range

Uniform MotionUniform Motion

Uniform Accelerated MotionUniform Accelerated Motion

Time of FlightTime of Flight

Maximum HeightMaximum Height

Etc.Etc.

What do the following situations have What do the following situations have in common?in common?

A truck is equipped with a flare A truck is equipped with a flare launcher which is capable of launcher which is capable of launching a sphere vertically launching a sphere vertically (relative to the truck). (relative to the truck).

A relief package drops from a low-A relief package drops from a low-flying airplane.flying airplane.

1.1. Suppose a truck is equipped with a flare Suppose a truck is equipped with a flare launcher which is capable of launching a sphere launcher which is capable of launching a sphere vertically (relative to the truck). If the truck is in vertically (relative to the truck). If the truck is in motion and launches the flare and maintains a motion and launches the flare and maintains a constant horizontal velocity after the launch, constant horizontal velocity after the launch, then where will the flare land (neglect air then where will the flare land (neglect air resistance)?resistance)?a. in front of the truck a. in front of the truck b. behind the truckb. behind the truckc. in the truckc. in the truck

http://www.physicsclassroom.com/mmedia/vectors/tb.cfm

2. Suppose a rescue airplane drops a relief 2. Suppose a rescue airplane drops a relief package while it is moving with a constant package while it is moving with a constant horizontal speed at an elevated height. horizontal speed at an elevated height. Assuming that air resistance is negligible, Assuming that air resistance is negligible, where will the relief package land relative to where will the relief package land relative to the plane?the plane?

a. below the plane and behind it. a. below the plane and behind it. b. directly below the planeb. directly below the planec. below the plane and ahead of itc. below the plane and ahead of it

http://www.physicsclassroom.com/mmedia/vectors/pap.cfm

Lesson sequenceLesson sequenceDay 2 and 3Day 2 and 3

Description of Activity Teaching/LearningStrategies

ExpectationsAddressed

Learning Styles Assessment

Day 2 and 3:1. Discuss how objects

release from the same height and projected horizontally and with different masses hit the ground the same time.

2. Parabolic motion and angle of projection

3. Comparing Horizontal Range :Using formula to verify maximum possible range using different angles and a fixed initial velocity

-Demo- usingtwo objectWithDifferentmasses

-Animation

InvestigationGroup workTextbook

B2.1B2.2

VisualAuditoryKinesthetic/TactileInterpersonal

Formative- Checking for

understanding- Questioning of

students based on their mathematical knowledge

- Solve for maximum range using formula

-concept quiz

Description of Activity Teaching/LearningStrategies

ExpectationsAddressed

Learning Styles

Assessment

Day 4: 1.Problem Solving-Analyzing the motion of objects projected horizontally-Analyzing more complex projectile motion-Class work

-Direct Instruction,student involve-Problem Solving Strategies-Independent work -Compiling Physics Toolbox

B2.1B2.2B2.3

KinestheticVisualAuditory

Formative-Circulate while students individually solve problems to observe students’ readiness-Concept Circle-Parallel Questioning-assignmentSummative-Quiz, Test

Lesson sequenceLesson sequenceDay 4Day 4

Concept CircleConcept Circle

Modify the strategy by:Modify the strategy by: leaving one section empty, leaving one section empty,

to be filled by students;to be filled by students; including one non-example including one non-example

and asking students to find and asking students to find which item does not which item does not belong and to justify their belong and to justify their answer.answer.

Concept:____________

Physics ToolboxKinematics Equations for Projectile Motion

Description Formula

Horizontal (x) Motion

Vertical (y) Motion

Quadratic Formula

Horizontal Range

etc etc

Differentiating Physics InstructionDifferentiating Physics InstructionParallel QuestionsParallel Questions

Task 1Task 1 Task 2Task 2A child travels down a water slide, leaving it with a velocity ofA child travels down a water slide, leaving it with a velocity of4.2 m/s horizontally. The child then experiences4.2 m/s horizontally. The child then experiencesprojectile motion, landing in a swimming poolprojectile motion, landing in a swimming pool3.2 m below the slide.3.2 m below the slide.(a) For how long is the child airborne?(a) For how long is the child airborne?(b) Determine the child’s velocity upon entering the water.(b) Determine the child’s velocity upon entering the water.

A helicopter, travelling horizontally, is 82 m above theA helicopter, travelling horizontally, is 82 m above theground. The pilot prepares to release a relief packageground. The pilot prepares to release a relief packageintended to land on the ground 96 m horizontally ahead. Airintended to land on the ground 96 m horizontally ahead. Airresistance is negligible. The pilot does not throw the package,resistance is negligible. The pilot does not throw the package,but lets it drop. What is the initial velocity of the packagebut lets it drop. What is the initial velocity of the packagerelative to the ground?relative to the ground?

Misconception # 1Misconception # 1

Students develop personal “theories of motion” by generalising the ideas they acquire from observation of objects in everyday situations (Keeports, 2000)

Heavier objects fall fasterHeavier objects fall faster..

Addressing Misconception # 1Addressing Misconception # 1 Animation are useful tools Animation are useful tools

for visual learners. for visual learners. Here we see that heavier Here we see that heavier

objects hit the ground at objects hit the ground at the same time as lighter the same time as lighter ones. ones.

http://library.thinkquest.org/2779/


If one object is dropped from a If one object is dropped from a specific point and another is specific point and another is projected forward from the same projected forward from the same point, then the projected object will point, then the projected object will take longer to reach the ground.take longer to reach the ground.

Let’s Consider…Let’s Consider…

Ball A falls freely from a specific height and at Ball A falls freely from a specific height and at the same time ball B is thrown horizontally the same time ball B is thrown horizontally from the same height. from the same height.

(a) How do we compare the acceleration of the (a) How do we compare the acceleration of the two balls. two balls.

(b) Which ball will hit the ground first? Why?(b) Which ball will hit the ground first? Why?

Nelson: Physics 12 p.41

Addressing Misconception # 2Addressing Misconception # 2

This animation shows This animation shows that both objects that both objects reach the ground at reach the ground at the same time.the same time.

this illustrates the this illustrates the concept in a different concept in a different way for Visual way for Visual learnerslearners

Nelson: Physics 12 p.41http://library.thinkquest.org/2779/

Misconception # 3 Misconception # 3 Parabolic MotionParabolic Motion

Showing the parabolic nature of projectiles Showing the parabolic nature of projectiles leads the student to believe they are quite leads the student to believe they are quite different from linear falling or horizontal different from linear falling or horizontal motionmotion


An easy way to deal with this is to plot the motion An easy way to deal with this is to plot the motion of a freely falling object and a horizontally moving of a freely falling object and a horizontally moving object on the same graph. object on the same graph.

When the intersection points at the same time, When the intersection points at the same time, are connected, the result is a parabola.are connected, the result is a parabola.


The The greengreen ball illustrates ball illustrates uniform motionuniform motion

The The redred ball illustrates free ball illustrates free fall and uniform accelerated fall and uniform accelerated motionmotion

The combination of these two The combination of these two motions at equal time motions at equal time intervals yields the parabolic intervals yields the parabolic path shown by the path shown by the blueblue ball! ball!

Horizontal and vertical Horizontal and vertical motion are independent of motion are independent of each othereach other

http://www.physicsclassroom.com/mmedia/vectors/bds.gif

Misconception # 4 Misconception # 4 Parabolic MotionParabolic Motion

At the top (peak) of its trajectory, the At the top (peak) of its trajectory, the velocity of a projectile is always momentarily velocity of a projectile is always momentarily zero. zero.

The acceleration of the object is also zero, at The acceleration of the object is also zero, at the peak.the peak.

Let’s ConsiderLet’s Consider

A basketball ball is thrown at an angle from one A basketball ball is thrown at an angle from one person to another. person to another.

1.1. What is the velocity of the object at the peak What is the velocity of the object at the peak of the flight? of the flight?

2.2. What is the acceleration of the object at the What is the acceleration of the object at the peak of the flight?peak of the flight?

Addressing Misconceptions # 4Addressing Misconceptions # 4 Have students look at the horizontal and vertical velocity vectors Have students look at the horizontal and vertical velocity vectors

throughout parabolic flight. throughout parabolic flight. Demonstrate that the velocity is not zero as there must be some Demonstrate that the velocity is not zero as there must be some

horizontal motion still (it doesn’t stop in midair).horizontal motion still (it doesn’t stop in midair).

# 4 Cont’d# 4 Cont’d If you throw an object in the air, it stops briefly (vertical If you throw an object in the air, it stops briefly (vertical

velocity is zero) but acceleration is not zero (gravity doesn’t velocity is zero) but acceleration is not zero (gravity doesn’t stop). stop).

What is its role? What is its role? To change the direction of the velocity vector.To change the direction of the velocity vector.

http://www.physicsclassroom.com/Class/vectors/U3L2c.cfm


Students believe that the greater the angleStudents believe that the greater the angleof projection, the greater the horizontalof projection, the greater the horizontaldistance travelled by a projectile.distance travelled by a projectile.

Class Activity Nelson Physics 12: Class Activity Nelson Physics 12: Comparing Horizontal Range p.49Comparing Horizontal Range p.49Use formula to verifyUse formula to verify

http://www.physicsclassroom.com/mmedia/vectors/mzi.cfm

Can you spot the Mistake in this animation?

Strategies for solving problems

Frame the Problem Identify the Goal Variables and Constants

Involved in the problem Known Implied Unknown

Strategy Calculations Validate

McGraw-Hill Ryerson Physics 11

Applications and Societal Applications and Societal ImplicationsImplications

SportsSports Projectile WeaponsProjectile Weapons Forensic Forensic Forest FireForest Fire Circus/fireworksCircus/fireworks Drop food in disaster areasDrop food in disaster areas

Assessment and EvaluationAssessment and Evaluation

AssignmentAssignment QuizQuiz TestTest LabLab

Monkey and Banana Monkey and Banana ProblemProblem

Monkey and BananaMonkey and BananaThrow at the Monkey in a Gravity Free Environment


Throw above the Monkey with Gravity On


Throw at the Monkey at a Fast Speed with Gravity On


Throw at the Monkey at a Slow Speed with Gravity On


ReferencesReferences

http://www.lon-capa.org/~mmp/kap3/cd060.htm http://www.walter-fendt.de/ph14e/projectile.htm http://www.falstad.com/mathphysics.html http://www.physicsclassroom.com/mmedia/vectors/mzi.cfm Keeports, D. (2000). Addressing physical intuition-a first day event. The

Physics Teacher,38, 318-319.

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