Soccer Kicks: A Real vs. Ideal Projectile Motion Experiment
1 Hook: Can we use the equations we learned in class to predict the flight of a soccer ball? Do the equations really work in real life (in your favorite sport)?
The teacher will lead a sports discussion to pique student interest in the activity. Any sport with a launched ball is appropriate (e.g. football, soccer, baseball). The teacher will use questioning tactics to engage students and elicit responses to, including but not limited to:
1. How many of you play a sport such as football, baseball or soccer?
2. Have you ever watched a game on TV, such as baseball or football, where the announcers give statistics about the ball (e.g. hang time of a football punt, or the distance a home run ball traveled?)
3. Do you think the kinematic equations/functions we derived in class, which typically apply to ideal conditions, could be used to calculate the trajectory of a real, launched ball?
4. How accurate do you think these equations are in a "real-life" situation? In other words, do you think there's any difference in our predicted values vs. the real world measurements?
5. To find out, we should generate some data, visualize and analyze it and draw our own conclusions.
After the motivating discussion, the students are invited to visit YouTube.com for a few minutes (teacher discretion) and search for soccer, football or baseball highlights that show the characteristics of projectile motion as previously discussed in class. Specifically, students should note any discrepancies and departures from the ideal cases we have been studying in class and solving as homework problems.
2 Direct Instruction: How We Will Collect Our Data
The teacher will explain the steps required in order for each team of three students to collect data that will be used for analysis, including how to:
- download the Adidas Snapshot app (free, iOS and Android) to their smartphone or other device from the appropriate app store.
- use the app to record and collect data (speed and launch angle) for a soccer kick.
- apply the proper equation derived in class that predicts the range of the ball and show the appropriate number substitutions from the app data, including converting units (mi/hr to m/s)
- measure the actual distance the ball travels in meters
- work with a team to enter in their data points into a shared resource such as Excel Online or Google Sheets or Tableau Public
- create a data visualization that allows students to discover trends
- form a conclusion when comparing the ideal vs. real measurements
- communicate the results of the experiment in an appropriate digital form
Students will need to complete the following steps in order to be successful (note: students may collect multiple data points as time permits):
- Students should download the Adidas Snapshot app to their smartphone or other device prior to reporting to the athletic fields for this activity.
- Students should review the range equation as derived in class, and practice its use with a sample problem provided by the teacher.
- Students should review the factor label method to convert miles per hour (mi/hr) to meters per second (m/s) with a sample problem provided by the teacher. Students should have access to their laptops/Chromebooks and the shared spreadsheet document for the data entry and analysis part of the experiment.
3 Guided Practice: Collecting the Data
Teacher should accompany students to the athletic fields or other open area, distribute soccer balls to each team of three and monitor student work. Teacher should provide technical and organizational assistance as needed while students generate and record the data for this experiment.
- Students should work in teams of three: person one will take the kick, person 2 will use the app to collect the launch data (speed and angle) while person 3 watches the flight of the ball and locates its landing spot. (These roles will alternate so all get a turn to kick the ball and record a data set. Multiple kicks may be taken as time allows or as desired by your teacher.)
- In a lab notebook, person 2 should record the launch speed in miles per hour (mi/hr) and angle (in degrees) as reported by the app while person 3 measures and records the distance the ball traveled in meters.
- Students should rotate their roles in the group until all have had a chance to kick. If time allows, continue taking data until your teacher directs you to stop.
- Once the required data has been collected, return to the classroom to perform your calculations and analyze your data.
4 Independent Practice: Data Analysis and Conclusions
The teacher will provide a spreadsheet template for students to contribute their data. Aggregate data will be used so students can see trends and patterns more readily. Teacher should provide assistance as needed. After data has been entered, teacher should direct students to download a copy of the aggregate data so each team can create a data visualization and perform their analysis of the data independently.
- Students will enter two data points into the shared spreadsheet document: the calculated (ideal) range and the actual (real), measured range. Therefore, students must use the range formula from the kinematic equations to calculate the predicted range.
- To calculate the ideal range: From the app data, you will have a launch speed in miles per hour (mi/hr). For the range equation to work properly, this speed must be converted to the base SI unit of meters per second (m/s). Use the factor label method to perform this conversion.
- Now that you have the speed in units of m/s, apply the range equation by substituting in the proper values. Recall the range equation derived previously in class: R = [ Vo^2 * sin(2*Ø) ] / g, where Vo is the launch velocity in m/s, Ø is the launch angle in degrees, and g = 9.8 m/s/s, the acceleration due to gravity.
- In the common spreadsheet document, enter your value from step 8 above into the "Ideal" column, and the measured value of the range in the "Real" column.
- Repeat steps 2, 3 and 4 until all your data is entered.
- When the entire class has finished entering their data, your team should download a copy of the spreadsheet so you may begin analyzing your data.
- Your task is to turn the spreadsheet with columns of numbers into a data visualization. You might choose a scatter plot graph, histogram, etc. Your team should decide what visualization best illustrates the trend and relationship between the numbers. Be creative here!
- From your visualization, discuss what conclusions you might reliably draw from the presented data. Be sure to account for all the trends you might find, and include a plausible explanation for any outliers you might observe.
5 Wrap-up: Reporting Your Experimental Results
The teacher will provide guidance and assist students as needed to create their final project in order to report their results. Students should be prepared to present their projects and findings in a 5 minute presentation to the class. Teacher should encourage creativity in the data visualizations and allow any appropriate tool for the final project.
Students should create a coherent, visually interesting and scientifically sound presentation to report their findings to the class. Specifically, your project must include:
- An explanation of the problem to be investigated.
- A description of your experimental method.
- The data that was collected.
- The calculations that were necessary.
- A visualization of the dataset.
- The analysis of your data.
- The conclusions you drew from your data: Do the equations used in class to predict the ideal behavior of a projectile match the observed results in the "real world?" Defend your answer with credible causes for any discrepancies, including any outliers.
- Questions to consider: From the same experimental setup, are there other data points that could be collected? What trends might they show? Can you propose an extension to this experiment?
You may complete this project with a Prezi, PowerPoint deck, Tableau visualization, iMovie, etc. The choice is yours: Be convincing and be creative! Good luck!
Key Standards Supported
|RST.11-12: Integration of Knowledge and Ideas|
|RST.11-12.9||Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible.|
|WHST.11-12: Research to Build and Present Knowledge|
|WHST.11-12.9||Draw evidence from informational texts to support analysis, reflection, and research.|
|8.F: Use Functions To Model Relationships Between Quantities.|
|8.F.4||Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.|
|8.F.5||Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.|
|HSF.IF: Interpret Functions That Arise In Applications In Terms Of The Context|
|HSF.IF.4||For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★|
|HSF.IF.5||Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★|
|HSF.IF.6||Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★|
Linear, Quadratic, And Exponential Models
|HSF.LE: Interpret Expressions For Functions In Terms Of The Situation They Model|
|HSF.LE.5||Interpret the parameters in a linear or exponential function in terms of a context.|
|HSF.TF: Prove And Apply Trigonometric Identities|
|HSF.TF.8||Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to calculate trigonometric ratios.|
|HSF.TF.9||(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.|
Vector And Matrix Quantities
|HSN.VM: Represent And Model With Vector Quantities.|
|HSN.VM.1||(+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).|
|HSN.VM.2||(+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.|
|HSN.VM.3||(+) Solve problems involving velocity and other quantities that can be represented by vectors.|
Key Standards Supported
|HS-ETS1-2||Design a solution to a complex real-world problem by breaking it down into smaller, more manageable problems that can be solved through engineering.|
Motion and Stability: Forces and Interactions
|HS-PS2-1||Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.|
|HS-PS2-4||Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.|