Projectile Motion by Jason Kozel

Transformation 2013 Design Challenge Planning Form Guide Design Challenge Title: Projectile Forensics Teacher(s):Pamela Miller School: Harlandale High School Subject: Two-dimensional motion: Projectile motion Abstract: Students have been recruited by the Crime Scene Investigation division of their local police department to use their knowledge of projectile motion to solve a crime that took place in the community.

MEETING THE NEEDS OF STEM EDUCATION THROUGH DESIGN CHALLENGES

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Begin with the End in Mind The theme or â&#x20AC;&#x153;big ideasâ&#x20AC;? for this design challenge: Students will apply projectile motion concepts to real world situations. TEKS/SEs that students will learn in the design challenge: (4) Science concepts. The student knows the laws governing motion. The student is expected to: (B) analyze examples of uniform and accelerated motion including linear, projectile, and circular; Key performance indicators students will develop in this design challenge: Vocabulary development ( projectile motion, projectile range, x components, y components, velocity, acceleration, displacement; apply linear motion equations to the horizontal and vertical components of a projectile; calculate elapsed time, vertical displacement, horizontal displacement, horizontal velocity, vertical velocity, vertical acceleration; use projectile motion knowledge to locate the origin of a bullet shot into the air 21st century skills that students will practice in this design challenge: www.21stcenturyskills.org Communication, collaboration, critical thinking, problem solving STEM career connections and real world applications of content learned in this design challenge:

Career: Forensic scientist Connections: Students will be able to explain how projectile motion concepts apply to situations in the real world such as forensics, sports, etc.

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The Design Challenge It is the morning of January 1st. During the New Yearâ&#x20AC;&#x2122;s celebration the night before, celebratory shots were fired into the air in your neighborhood. You heard the shots, but they were distant. Your neighbors, the Smiths, woke up to find their five year old bull dog dead of a gunshot wound. Your neighbors are well liked in the neighborhood, as was their dog. You begin to think that the celebratory shots heard the night before may have had something to do with the incident. The local police department is intrigued by your theory and introduces you to the crime scene investigators on the case. The police are taking the incident very seriously because these random gunshots could have killed anyone. It is your job to help the crime scene investigators pinpoint the location at which the shots originated.

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Map the Design Challenge Performance Indicators

1. Vocabulary development ( projectile motion, projectile range,

x components, y components, velocity, acceleration, displacement) 2. Apply linear motion equations to the horizontal and vertical components of a projectile 3. Calculate elapsed time, vertical displacement, horizontal displacement, horizontal velocity, vertical velocity, vertical acceleration 4. Use projectile motion knowledge to locate the origin of a bullet shot into the air

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Already Learned

Taught before the project

Taught during the project

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Team-Building Activity It is important that teachers provide team-building activities for students to help build the 21st Century Skills that are necessary for success in the workforce. Team-building helps establish and develop a greater sense of cooperation and trust among team members, helps students adapt to new group requirements so that they can get along well in a new group, serves to bring out the strengths of the individuals, helps identify roles when working together, and leads to effective collaboration and communication among team members so that they function as an efficient, productive group. Our students are often not taught how to work in groups, yet we assume that they automatically know how. Use team-building activities with your students so that you can see the benefits which include improvement in planning skills, problem solving skills, decision making skills, time management skills, personal confidence, and motivation and morale.

Multi-Way Tug-of-War 

Choose an indoor or outdoor location, but make it a soft location (e.g. grass).

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In multi-way tug-of-war it is mostly the use of tactics that wins, combined with some strength, whereas the opposite is true in traditional tug of war.

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Lay out the ropes. Four ropes (30-60 ft long) should be attached to a center ring.

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Divide into groups and make sure the groups appear to be of similar strength.

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Brief group on normal tug-of-war safety rules, basically: o

no wrapping or tying rope around anyone or anything - only hold rope with hands

watch out for rope burn on hands - let go if rope is moving through hands

watch out for rope burn on body - let go if you lose footing

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First command from the Tug-of-War master is "pick up the slack". The Tug-of-War master makes sure the centre ring is stable and centered. This needs strong leadership because teams are always keen to add extra strain!

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Second command is "Go!!"

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Teams attempt to pull the center ring or knot over their finish line. This can rarely be achieved by strength alone and instead will require guile. Teams can swivel to cooperate / compete with other teams, then switch directions, etc.

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Conduct several rounds. Continue, say, until one team earns 3 victories and the Tug-of-War title.

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Allow teams plenty of time to physically recover and debrief/plan after each round.

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Team building groups may wish to discuss what the secrets to success were in this activity - and whether these lessons apply elsewhere.

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5E Lesson Plan Design Challenge Title: Projectile Forensics TEKS/TAKS objectives: §112.47. Physics 4B Engage Activity Monkey and Hunter Computer Simulation http://physics.bu.edu/~duffy/semester1/c04_monkeyhunter.html Present the situation to the students. Have them write in their journals 3-5 sentences hypothesizing the best place to aim in order to hit the monkey. Survey the students and discuss why they have made their choices. Play the simulation for each of the three aiming options. Discuss how the correct answer demonstrates two important principles of projectile motion (1) horizontal and vertical motion are independent of each other and (2) all objects accelerate towards the ground at the same rate. Have students reflect on the demonstration and the conclusions they have reached. This demonstration can also be done with a ballistic pendulum. Introduce the challenge: It is the morning of January 1st. During the New Year’s celebration the night before, celebratory shots were fired into the air in your neighborhood. You heard the shots, but they were distant. Your neighbors, the Smiths, woke up to find their five year old bull dog dead of a gunshot wound. Your neighbors are well liked in the neighborhood, as was their dog. You begin to think that the celebratory shots heard the night before may have had something to do with the incident. The local police department is intrigued by your theory and introduces you to the crime scene investigators on the case. The police are taking the incident very seriously because these random gunshots could have killed anyone. It is your job to help the crime scene investigators pinpoint the location at which the shots originated. Students will work in pairs to solve the challenge. Students will make an initial report on the information presented in the crime scene notes. Engage Activity Products and Artifacts Monkey and Hunter Journal Entry Initial Crime Scene Report

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Engage Activity Resources http://physics.bu.edu/~duffy/semester1/c04_monkeyhunter.html

Explore Activity Simulation: This activity can be done either with the whole class, individually, or in pairs depending on the number of computers available. http://phet.colorado.edu/sims/projectile-motion/projectile-motion.swf Explore the simulation. Through out the course of your exploration, answer the following questions.  Neglecting air resistance, what is the angle at which an object hits the target at its original location?  What angle of launch causes the projectile to travel the farthest?  How does air resistance affect height and range of the projectile? Hands-on: Can you design and launch an air powered rocket to hit a target 5 m away? Students should answer these questions as they design and launch their rocket:  How did air resistance factor into the design of your rocket? The launch?  What variables affect the distance your rocket travels when launched?  Explain why you chose the materials used for your rocket. Explore Activity Products and Artifacts Lab notes for simulation Lab notes for hands-on activity Explore Activity Materials/Equipment Computer(s) with internet access, projector, rocket building materials (a variety of paper, different types of tape, at least two different sizes of straw, pvc pipe, clay, 1, 2 and three liter soda bottles, etc) Explore Activity Resources http://phet.colorado.edu/sims/projectile-motion/projectile-motion.swf Air rocket building: http://www.eweek.org/site/pdfs/English/07_BottleRocket.pdf http://space.about.com/od/activities/ss/bottlerocket.htm http://www.sciencetoymaker.org/airRocket/index.html

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Explain Activity Students will take Cornell notes during the “Projectile Motion” PowerPoint presentation. Students will complete “Projectile Motion Calculations” for homework. Explain Activity Products and Artifacts Cornell notes for “Projectile Motion” PowerPoint presentation “Projectile Motion Calculations” homework Explain Activity Materials/Equipment Computer with PowerPoint, projector, “Projectile Motion” PowerPoint presentation, calculators Explain Activity Resources “Projectile Motion” PowerPoint Instructions for Cornell notes http://coe.jmu.edu/learningtoolbox/cornellnotes.html Projectile Motion Practice Problems: http://www.jburroughs.org/science/mschober/2dmotion/practice.htm http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/vectors/u3l2e.html http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/vectors/u3l2f.html www.rockdale.k12.ga.us/personal/rgluesing/physics/Handouts/Projectile%20Motion%20Practice%20Pro blems.doc

Elaborate Activity

Lab: Projectile Motion with Arrows This lab could also be done with Nerf cannons or dart guns. Working in groups of 2-3, students go out to the bleachers next to the football field/track with a bow and arrow (possibly obtained from physical education department). Part 1: Climb to the top of the bleachers. Shoot the arrow horizontally into the field. Make the following measurements/calculations and diagram the situation. Be sure to use metric units for all measurements and calculations. Length of bleachers Height of bleachers Calculated time in air Range of the arrow Calculated release velocity

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Part 2: Lying on the football field, shoot the arrow at an angle. Make the following measurements/calculations and diagram the situation. Be sure to use metric units for all measurements and calculations. Calculated Angle of Release Release velocity as calculated in Part 1 Calculated time in the air Calculated Range Actual Range Calculated average velocity Percent difference between calculated horizontal and angled velocities Crime Scene Research Students will research information about bullet trajectories, ballistics, and projectile motion. Students will take notes on their research, and then apply what they have learned to their Final Crime Scene Report. Elaborate Activity Products and Artifacts Lab: Projectile Motion with Arrows Research notes Elaborate Activity Materials/Equipment Bow and Arrow for each group, Calculators for each group, Access to bleachers, Protractors, Computers will internet access for each pair of students, library access Elaborate Activity Resources http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html http://www.worsleyschool.net/science/files/bullet/trajectory.html http://www.worsleyschool.net/science/files/projectiles/projectile.html http://www.physics-lab.net/applets.php?app=projectile

Evaluate Activity Students will complete the “Final Crime Scene Report.” Students will need to include calculations supporting their conclusions. The “Final Crime Scene Report: Rubric” should be given to students before they begin. Evaluate Activity Products and Artifacts Final Crime Scene Report

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Evaluate Activity Materials/Equipment “Final Crime Scene Report: Rubric” handout, calculators Evaluate Activity Resources “Final Crime Scene Report: Rubric” handout

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Projectile Forensics The Scenario: It is the morning of January 1st. During the New Year’s celebration the night before, celebratory shots were fired into the air in your neighborhood. You heard the shots, but they were distant. Your neighbors, the Smiths, woke up to find their five year old bull dog dead of a gunshot wound. Your neighbors are well liked in the neighborhood, as was their dog. You begin to think that the celebratory shots heard the night before may have had something to do with the incident. The local police department is intrigued by your theory and introduces you to the crime scene investigators on the case. The police are taking the incident very seriously because these random gunshots could have killed anyone. It is your job to help the crime scene investigators pinpoint the location at which the shots originated. Crime Scene Notes: The bullet extracted from the dog has been matched to a Remington 870 shotgun. This gun releases bullets with an exit velocity of 375 m/s. The bullet entered the dog at an angle 85 degrees from the horizontal. There are three suspects in the neighborhood that are registered owners of Remington 870 shotguns: Arthur Jones

Lives 0.5 miles away Arthur has a record of noise violations for loud parties he frequently holds at his residence.

Sean Carson

Lives 3.0 miles away Has no criminal record

Hank Rogers

Lives 5.0 miles away Hank has a record that includes possession of a controlled substance and grand theft auto. Hank has served time in prison and was released after completing his sentence.

The dog was lying on the Smiths’ deck when he was shot. The deck is 1.75 m above the ground. There was no other evidence of the shooter at the Smiths’ residence.

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Initial Report: Based on the information collected at the scene, describe how you plan to proceed. Include a discussion of the suspects and other information from the scene. What do you feel is the most important piece of information or evidence? (Minimum of 1 paragraph, 5-7 sentences) ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

Research: Research information on bullet trajectories, forensic ballistics and projectile motion. Remember, your goal is to identify the perpetrator from the list of suspects. You will be expected to show calculations that support your accusations. Attach additional sheets if necessary. ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________

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Projectile Motion Calculations Directions: Draw a diagram for each situation. Use equations for projectile motion to solve each problem. For all calculations, ignore air resistance. 1. You throw a baseball horizontally. You release it from a height of 1.8 m and it lands 20 m away. How long was the baseball in the air? How fast did you throw it?

5. You are protecting a fort from intruders. You are manning a cannon at the top of a 35 m tower. Your cannon fires the cannonball with a horizontal velocity of 115 m/s. How much time does it take for the cannonball to reach the ground? How far does the cannonball travel?

5. You are learning to juggle. You throw a ball straight up into the air. It takes 1.5 s to reach its peak. You catch the ball at the same height you threw it from. How many seconds does it take to fall from its peak back into your hand?

4. A baseball player hits a home run. It just clears the fence 100m from home plate. The fence is 3.00 m higher than the height at which the ball was hit. The ball left the bat at an angle of 33Â° above the horizon. At what speed did the ball leave the bat?

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5. You are playing soccer with your friends. You kick the ball toward the goal, 2.00 meters from the goal. You kick the ball at a 75Â° angle above the horizon with a velocity of 11.7 m/s. How long does it take to reach the goal? At what height is the ball when it reaches the goal?

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Plan the Assessment Engage Artifact(s)/Product(s): Monkey and Hunter Journal Entry, Initial Crime Scene Report

Explore Artifact(s)/Product(s): Lab notes for simulation, Lab notes for hands-on activity

Explain Artifact(s)/Product(s): Cornell note for “Projectile Motion” PowerPoint presentation, “Projectile Motion Calculations” homework

Elaborate Artifact(s)/Product(s): Lab: Projectile Motion with Arrows, Research Notes

Evaluate Artifact(s)/Product(s): Final Crime Scene Report

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Rubrics Final Crime Scene Report: Rubric Your report should include who you think the perpetrator is, and how you came to that conclusion. You should include a one paragraph (5-7 sentences) explanation of how you applied principles of projectile motion to make your accusations. Attached to your explanatory paragraph should be all the calculations used to reach your conclusions. Calculations should include diagrams/sketches. Student Name:

________________________________________

CATEGORY Explanation

4 Explanation is detailed and clear.

3 Explanation is clear.

2 Explanation is a little difficult to understand, but includes critical components.

1 Explanation is difficult to understand and is missing several components OR was not included.

Projectile motion Concepts

Explanation shows complete understanding of the projectile motion concepts used to solve the problem(s).

Explanation shows substantial understanding of the projectile motion concepts used to solve the problem(s).

Explanation shows some understanding of the projectile motion concepts needed to solve the problem(s).

Mathematical Reasoning

Uses complex and refined mathematical reasoning.

Uses effective mathematical reasoning

Some evidence of mathematical reasoning.

Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written. Little evidence of mathematical reasoning.

Mathematical Errors

90-100% of the steps and solutions have no mathematical errors.

Almost all (8589%) of the steps and solutions have no mathematical errors.

Most (75-84%) of the steps and solutions have no mathematical errors.

More than 75% of the steps and solutions have mathematical errors.

Diagrams and Sketches

Diagrams and/or sketches are clear and greatly add to the reader's understanding of the procedure(s).

Diagrams and/or sketches are clear and easy to understand.

Diagrams and/or sketches are somewhat difficult to understand.

Diagrams and/or sketches are difficult to understand or are not used.

Neatness and Organization

The work is presented in a neat, clear, organized fashion that is easy to read.

The work is presented in a neat and organized fashion that is usually easy to read.

The work is presented in an organized fashion but may be hard to read at times.

The work appears sloppy and unorganized. It is hard to know what information goes together.

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Story Board  

Week 1 Activities

Day 1 Multi- way Tug of War (30 min) Monkey and Hunter Engage Activity (1520 min)

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Week 2 Activities 

Day 6 Part 2 of “Projectile Motion with Arrows” lab (35 min) Debrief of lab

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Day 2 Introduce challenge: Projectile forensics (15 min) Assign Homework: Initial crime Scene Report (5 min) Explore simulation (20 min)

Day 7 Crime Scene Research (45 min)

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Day 3 Explore Hands on (45 min)

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Day 8 Work on Final report, finish for homework (45 min)

Day 4 Explain “Projectile Motion” PowerPoint with Cornell Notes (35 min) Begin “Projectile Motion Calculations” Finish for homework (15 min)

Day 9

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Day 5 Go over “Projectile Motion Calculations” homework (15 min) Part 1 of “Projectile Motion with Arrows” Lab (35 min)

Day 10

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