HPP A13v1 Modeling Your Motion When Airborne
 Review the Hints for Using Excel (Reference E) before coming to this lab.
Last lab you studied the motion of a person as they jumped straight up and down in the air. This lab you are going to expand this study to see what motion results when a person (like a diver) pushes off sideways at the same time as jumping up and becomes airborne. To help you with this investigation, you are also going to be introduced to two pieces of software that will simplify your analyses quite a lot. To get things started, you will first try out this new software to study the motion of a falling croquet ball.
Your instructor will show you videos of two falling croquet balls. Watch these videos carefully and discuss the following questions based on your observations.
In words describe the motion of the two balls in the videos. Let's refer to them as the
"right croquet ball" and the "left croquet ball" so everyone can keep them straight. When you discuss the motion, be sure to identify to which ball you are referring.
Your instructor introduced the idea of frame rate. If a movie was filmed at a rate of 24 frames/s, then how much time passed between frames 3203 and 3217?
Start up the computer at your station and open the movie file named 1-Falling balls
Movie. Watch the movie by pressing the play button. You can also step through the movie frame by frame by using the left and right arrow keys on the keyboard.
Relevant information:
 This movie was filmed at a rate of 625 frames/s, although some frames have been removed from this file so that only 5 remain.
 The croquet balls start at a height of 1.7 m above the floor.
 The initial frame (#00804) may not have been when the ball first started moving.
1. How much time has passed between the first two frames of this computer file? Explain.
2. (a) Compare the motion of the two balls in the vertical direction. That is, how do their up/down displacements compare during each of the frames?
(b) Compare the motion of the two balls in the horizontal direction. That is, how do their left/right displacements compare during each of the frames?
(c) Based on your observations, how does the vertical component of velocity of the left croquet ball compared to that of the right croquet ball? What is your evidence?
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(d) Based on your observations, how does the horizontal component of velocity of the left croquet ball compared to that of the right croquet ball? What is your evidence?
Now that you have a feel for the motion of the croquet balls, you are going to use this movie to learn to use the new software tools. To get started, complete the following steps…
 "Quit" the software that displayed the movie file.
 Open the file 2-Falling balls.vpt. This should start up the software named VideoPoint. You should be looking at the movie again as well as some software tools.
Data Collection
VideoPoint is software designed to help you analyze motion from videos. It has already been calibrated so it knows relative distances and the time between adjacent frames. You will now use this software to analyze in detail the motion of the left croquet ball (the one moving in both the x and y directions).
 Click on the "Collect Data" icon on the side bar.
 Carefully click on the location of the left croquet ball. Once you click, the software will automatically move you ahead to the next frame of the movie.
After you have clicked on the five positions, you can go back and adjust the position of your data if necessary. To do this, use the arrow keys to move to the frame where the adjustment is needed and use the arrows on the "Point Adjust" icon on the side bar.
Once you are satisfied with your five data points, then you should see the values of time, x-position, and y-position in the data table. Before you go any further, quickly record these values here (so you won't lose them in case you experience computer problems). This only needs to be recorded once per group.
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 Before you do anything else, save your work so you will not lose your data should there be computer problems. Select "Save As" from the "File" menu. Be sure to give the file a meaningful, appropriate name. Record the name of this VideoPoint file in your logbook.
 "Hide VideoPoint" using the Application menu in the uppermost right corner of the screen.
Ask your instructor for assistance if this is unclear.
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Data Analysis
The VideoPoint software should now be hidden. Start up the Excel file 3-Falling balls
Analysis.
Keep in mind that you can easily navigate back and forth between software programs by using the Application menu in the uppermost right corner of the screen.
Go back to the VideoPoint software using the Application menu. Bring the data table window to the front by selecting "Table" from the "Window" menu. Under the "Edit" menu, choose "Select All" to highlight the data and then select "Copy" from this same menu.
Hide VideoPoint again from under the Applications menu. Return to Excel. Click once on the cell A4 and select "Paste" from the "Edit" menu. Your data should now be in the spreadsheet. Ask your instructor for assistance if it did not work.
Before you do anything else, save your work so you will not lose your data should there be computer problems. Select "Save" from the "File" menu. Be sure to give the Excel file a meaningful, appropriate name. Record the name of this file in your logbook.
You can now use the power of Excel to create graphical and functional models of your data of displacement vs. time. You should start by creating models for x-component of
displacement vs. time using the following procedures.
Graphical and Functional Model #1 - x-component of displacement vs. time
 Click once on the "Graph Wizard" button.
 Step 1 - Make sure to select XY (Scatter) for the chart type and the Chart sub-type with no connecting lines.
 Step 2 - Click on "Series" and then the "Add" button. Enter a short, but meaningful name for the data. Using your mouse, select all of the cells containing the x values (time) and the y values
(x-position).
 Step 3 - Enter a name for the graphical model as well as a title for each axis.
 Step 4 - Select "Place object in Sheet 1" and then click on the "Finish" button.
You should now be looking at a graph of your data on the screen! Save the file again by clicking on "Save."
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Your lab instructor can help you make adjustments to the graph as necessary. You should be sure it is in the correct format (titles, axes, units, etc.) just like all other graphs you have made in lab. In addition, you should check that the data points really appear to represent your data values. You have now created a graphical model of the x-component of displacement as a function of time for this croquet ball.
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Making Mathematical Function Models with Excel
The Excel software can also help you determine a best-fit mathematical function for graphed data. Use the following directions to do a mathematical fit for your data.
 To mathematically fit data in Excel, first create a graph showing the relevant data. (You should have already done this!)
 Select this graph by clicking on it once. Choose "Add Trendline…" from the "Chart" menu.
 Choose the type of fit you would like. If you think a linear fit is best, then select "Linear." If it seems more like a quadratic, then select "Polynomial (2)."
 Click on "Options" and select "Display equation on Chart." You can also select "Display rsquared." This will tell you if you have a good fit or not. A perfect fit has R 2 =1 and a very poor fit has R 2 =0.
 Click "OK" once you have selected your choices above. Excel will then display the best-fit mathematical function for the data with the kind of function you specified.
Printing Your Models with Excel
 Once you are satisfied with your graphical and functional models, you are ready to print.
 Make sure that your graph is selected (the four corners will be highlighted if it is selected).
 Choose "Print…" from the file menu and print a copy for each member of your group.
 Affix this graph into your lab manual.
Don't forget…
 Once again, be sure the graph is in the right format (title, labels, units, etc.). You can write them in by hand if they are missing on the printout.
 Note! Excel does not understand physics, only numbers! Therefore, it will always write the mathematical function models in terms of y, x, and numbers. It is your responsibility to
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HPP A13v1 Modeling Your Motion When Airborne rewrite this function model in terms of the relevant physics (as described in Reference B).
Be sure to rewrite it with suitable variables and all appropriate units!
 Write your version of the mathematical model directly on your graph printout.
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Graphical and Functional Model #2 - y-component of displacement vs. time
Repeat the procedures on pages 3 &4 and create a graphical and mathematical function model of the y-component of displacement vs. time.
You should now have two graphical models and two functional models representing the motion of one falling croquet ball. Use these models and your knowledge of the projectile motion equations to answer the following questions (3 - 9). In each case, explain how you are able to determine the requested values.
Comparing the horizontal and vertical components of displacement
3. (a) From your models and your knowledge of the projectile motion equations, what was the initial displacement of this croquet ball in the horizontal direction?
(b) What was the initial displacement of the croquet ball in the vertical direction?
(c) Do these values make sense based on what you viewed in the videos? Explain.
Comparing the horizontal and vertical components of velocity
4. (a) From your models, what was the value of the initial horizontal component of the ball's velocity?
(b) Recall that velocity is the rate of change of position in time. In words, describe the horizontal component of the ball's velocity as a function of time.
(c) Write a mathematical function model (with appropriate constants, units, and variables) as a function of time for the horizontal component of the ball's velocity.
5. (a) What was the value of the initial vertical component of the ball's velocity?
(b) In words, describe the vertical component of the ball's velocity as a function of time.
(c) Write a mathematical function model (with appropriate constants, units, and variables) as a function of time for the vertical component of the ball's velocity.
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6. Compare the horizontal and vertical components of the velocity. How are the two aspects of the motion different?
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Comparing the horizontal and vertical components of acceleration
7. (a) What kind of function would best describe the horizontal component of the ball's acceleration?
(b) Using the constants found from your graphs, write a mathematical function model (with appropriate constants, units, and variables) for the horizontal
component of the ball's acceleration.
8. (a) What kind of function would best describe the vertical component of the ball's acceleration?
(b) Write a mathematical function model (with appropriate constants, units, and variables) for the vertical component of the ball's acceleration.
(c) Use your mathematical function model to estimate the acceleration due to gravity based on your data. How does this value compare to the accepted value of g = -9.81 m/s 2 ? (Hint: calculate the percent difference.)
9. Compare the horizontal and vertical components of the acceleration. How are the two aspects of the motion different?
 Save your files again and quit all of the software that is running.
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Now that you have a feel for how to use the new software tools, you are ready to analyze the motion of something more interesting than a falling croquet ball.
Before you get started, be sure you have quit all of the software. This will reset all of the files and make sure that you are starting fresh. You can click on the menu in the uppermost right cornet of the screen to verify that nothing is running but the Finder. Once you have quit all the software, open and play the file 4-Swan dive Movie.
Data Collection
 Quit the software that displayed the movie file.
 Open the file 5-Swan dive.vpt examine the movie in VideoPoint.
 Once again, use the VideoPoint data collection tool to collect data from the motion of the diver. You should use the white stripe on her bathing suit just above her hip as the point to measure in each frame.
 Save this file, giving it a meaningful name. Record this file name in your logbook.
Data Analysis
 Open the file 6-Swan dive Analysis in Excel.
 Copy and paste the data from VideoPoint into this Excel file. Be sure to save the Excel file once it includes your data and record the name of this file.
 Using Excel, create graphical and functional models of the horizontal and vertical components of the diver's displacement. That is, create 2 graphs and 2 function models.
 Include the printouts in your logbook, making sure to put the models into the correct format.
10. (a) Consider the horizontal component of the diver's velocity. Using your models and your knowledge of the projectile motion equations, estimate its value initially, at the highest point of the dive, and as she entered the water?
(b) Consider the vertical component of the diver's velocity. What was its value initially, at the highest point of the dive, and as she entered the water?
(c) Calculate the total velocity of the diver as she hits the water in m/s and miles/hour.
Describe how you think you would feel if you hit your head on the dashboard of your car if you were traveling at this velocity.
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HPP A13v1 Modeling Your Motion When Airborne
11. (a) Consider the diver's motion as projectile motion. Based on your experimental models and data, write four mathematical function models for this diver's motion
(all as functions of time):
(1) horizontal component of velocity, (2) vertical component of velocity,
(3) horizontal component of acceleration, and (4) vertical component of acceleration.
(b) Use your mathematical function model(s) to estimate the acceleration due to gravity based on your data. How does this value compare to the accepted value of g = -9.81 m/s 2 ? (Hint: calculate the percent difference.)
12. How is the motion of the diver similar to your motion as a jumper in last week's lab? How were these two motions different?
13. Which do you think is a better method for studying motion – using MBL sensors or using video analysis? Explain your choice.
 Shut down the computer at your station by selecting "Shut Down" from the
"Special" menu on the desktop.
 Motion with constant acceleration and falling objects (see Walker, Section 2-5 – 2-7)
 Vector components (see Walker, Section 3-2)
 Two-dimensional Kinematics (projectile motion) (see Walker, Chapter 4)
 Using Excel software (see Reference E)
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