"Do not be too timid and squeamish about your actions. All life is an experiment. The more experiments you make the better."
Ralph Waldo Emerson, "November 11 [1842]," Journals of Ralph Waldo Emerson
(18411844), Houghton Mifflin (1911), p. 302.
Preparation
Due 12:00 PM before start of lab
Prelab assignment 3 (*.html), 1 point
Equipment
whiteboards, markers
laboratory laptop, PASCO Capstone
Big Ideas
Objects undergoing projectile motion have zero horizontal acceleration and a constant horizontal velocity, independent of their vertical motion, which has a constant vertical acceleration and a changing vertical velocity. The vertical motion of an object undergoing projectile motion is identical to that of an object undergoing free fall. Motion tracking software can be used to analyze the motion of objects in videos.
Goals
Students work in (selfassigned?) groups to understand the independent nature of horizontal and vertical motion for projectiles.
Students learn how to use motion tracking software to analyze videos of plausible and implausible scenarios.
Students recognize plausible motion parameters for objects undergoing free fall and projectile motion, and how these parameters would be affected for objects that experience forces other than that of gravity during motion.
Tasks
(Record your lab partners' names on your worksheet for tasks 12, to be turned in at the end of today's lab for randomly selected grading for your group.)
1. Analysis of HorizontallyLaunched Billiard Ball Run the PASCO Capstone software package. From "Displays" on righthand side of screen, separately drag a "Movie" window and two "Graph" windows onto the blank center page. Resize the "Movie" window to take up a half of the page, and the two "Graph" windows to each take up onequarter of the page.
 Download this video resource to your desktop:
In the "Movie" window, select "Open Movie File," and open the video. Click on the "Enter video analysis mode" button. Move the origin of the xy axes to the starting point of the ball shot horizontally, and resize the calibration tool bracket to the height of the lab table on the left. Set the height to be "1.05 m" (this is an approximation, ideally a meter stick or knownsized object would be shown for reference in a video used for motion analysis).
 Click on the movie window "Properties" icon (shaped like a gear), select "Movie Playback" and change the "Playback Frame Rate" to "60" (this was shot in slow motion, at 60 frames per second). (If your movie window is very small, then the "Properties" gear icon will be hidden on the top right, under the ">>" symbol.)
(At this point, and at other critical points, be sure save this workspace as a file to the desktop. PASCO Capstone may freeze or crash, but you can then exit the program completely, and click on the saved file on the desktop to start where you left off.)
 Move the playback head to the start of the movie. Make sure that the "Automatically advance the frame after clicking the object" and "Magnify video around the cursor" option buttons are selected.
 For each frame, click on the center of the billiard ball. Because of recording artifacts, click on the center of leading blurred billiard ball image.
 On the vertical axes of the first graph window, click on "<Select Measurement>" and choose "Video Analysis > Object #1 > y, Object #1 (m)." Click on "Scale axes to show all data," and click on "Adjust scaling for data changes  select scaling behavior " and choose "Scale Both Axes (Keep All Data Visible)."
 Click on "Highlight range of points in active data," and resize the area to enclose all of the data points. Click on "Apply selected curve fits to active data  Select curve fits to be displayed" and choose "Quadratic: At^{2} + Bt + C."
 This software typically reports uncertainties with two significant figures. Truncate/round all results for the vertical motion parameters with just one uncertain significant figure (e.g., rewrite "−4.85 ± 0.18" to "−4.9 ± 0.2," or "0.0275 ± 0.0076" to "0.028 ± 0.008").
C = y_{0} = __________ ± __________ m.
B = v_{0y} = __________ ± __________ m/s.
A = (1/2)⋅a_{y} = __________ ± __________ m/s^{2}.
Note that this is just matching the variables from the quadratic curve fit equation:
y(t) = A⋅t^{2} + B⋅t + C,
with the vertical motion equation for free fall or projectile motion:
y(t) = (1/2)⋅a_{y}⋅t^{2} + v_{0y}⋅t + y_{0}.
 Is the sign for the value of the initial vertical position y_{0} of the billiard ball positive or negative (or zero)? Briefly explain how this is consistent with the placement of the origin in your video window.
Sign of y_{0}: [ + − 0 ]
Brief explanation:
 Is the sign for the value of the initial vertical velocity v_{0y} of the billiard ball positive or negative (or zero)? Briefly explain how this is consistent with the placement of the origin in your video window.
Sign of v_{0y}: [ + − 0 ]
Brief explanation:
 What is the numerical value of the vertical acceleration a_{y} of the billiard ball? (Make sure you have the correct positive or negative sign.)
a_{y} = __________ ± __________ m/s^{2}.
 On the vertical axes of the second graph window, click on "<Select Measurement>" and now choose "Video Analysis > Object #1 > x, Object #1 (m)." Click on "Scale axes to show all data," and click on "Adjust scaling for data changes  select scaling behavior " and choose "Scale Both Axes (Keep All Data Visible)."
 Click on "Highlight range of points in active data," and resize the area to enclose all of the data points. Click on "Apply selected curve fits to active data  Select curve fits to be displayed" and choose "Linear: mt + b."
Truncate/round all results for the horizontal motion parameters with just one uncertain significant figure:
b = x_{0} = __________ m.
m = v_{0x} = __________ m/s.
 Is the sign for the value of the initial horizontal position x_{0} of the billiard ball positive or negative (or zero)? Briefly explain how this is consistent with the placement of the origin in your video window.
Sign of x_{0}: [ + − 0 ]
Brief explanation:
 Is the sign for the value of the initial horizontal velocity v_{0x} of the billiard ball positive or negative (or zero)? Briefly explain how this is consistent with the placement of the origin in your video window.
Sign of v_{0x}: [ + − 0 ]
Brief explanation:
 Although the numerical value of the horizontal acceleration a_{x} of the billiard ball is not displayed, it should be equal to zero. Briefly explain how you can deduce this based on the characteristics of the horizontal position graph.
Brief explanation:
 Print out one copy of this page (with movie, y(t) graph and curve fit parameters, and x(t) graph and curve fit parameters). (Keep this page open, as you will still be using it to analyze the motion of the dropped billiard ball next.)
2. Analysis of Dropped Billiard Ball
Go back to the movie window, and click on "Create Tracked Object," and you should see "Object #2" displayed in the toolbar. Repeat steps 1(d)(g) above to analyze the vertical motion only of the dropped billiard ball. What are the vertical motion parameters for the dropped billard ball? (Truncate/round all results for the vertical motion parameters with just one uncertain significant figure.)
C = y_{0} = __________ ± __________ m.
B = v_{0y} = __________ ± __________ m/s.
A = (1/2)⋅a_{y} = __________ ± __________ m/s^{2}.
 What is the numerical value for the vertical acceleration a_{y} of the dropped billiard ball? (Make sure you have the correct positive or negative sign.)
a_{y} = __________ ± __________ m/s^{2}.
 Consider the following generalization:
"The vertical acceleration of a projectile launched horizontally is identical to the vertical acceleration of an object that is dropped from rest, assuming that the effect of air resistance is negligible." Is the effect of air resistance negligible, based on the evidence you collected from the two billiard balls? Explain your reasoning and provide evidence by include specific relevant numbers in this statement, such that it can be read (and cited) on its own without referring to the above calculations and numbers. (Consider the uncertainty of your vertical motion parameters.)
Brief concluding statement:
3. Analysis of ESPN Sport Science Recreation of "Kobe Car Jump"
(Done on whiteboard only, to be worked on and presented as a group.) In a Nike commercial to promote its Hyperdunk basketball shoes in 2008, NBA Lakers teammate Kobe Bryant appears to jump over an Aston Martin DB9 Volante just before it would run into him. (Consensus is that the video was faked.)
On the ESPN show Sports Science in 2009, stuntman Damion Poitier attempted to recreate this same stunt with by (i) jumping in the foreground as the car passes by in the background, or (ii) being suspended by a wire harness that pulls him up over the car as it passes under him. You will analyze the vertical motion parameters of each jump.
 Download these video resources to your desktop:
 Unassisted free jump (set "Playback Frame Rate" to 30 frames per second).
 Assisted wire jump (slow motion, set "Playback Frame Rate" to 150 frames per second).
When his body is fully extended just after jumping off of the ground, you can scale the height of Damion Poitier to be 1.93 m (given as 6'4" on his IMDB profile), and mark his hip joint to track his motion, as this is close to his center of mass. Only track his motion while his feet are not in contact with the ground.
(Due to the softwareintensive nature of today's lab, it is not necessary to write a procedure for your group whiteboard project other than to cite the software package used and what it was used for.)
 Record your data in a table for the vertical motion parameters (y_{0}, v_{0y}, a_{y}) for both Damion Poitier's unassisted and assisted jumps. Print out two screen captures, each with the corresponding motion tracking video window and vertical position graph window with curve fit parameters.
 Consider the following generalization:
"The vertical motion of the free unassisted jump corresponds closely to an object in free fall, while the vertical motion of the wire assisted jump has characteristics significantly different than an object in free fall." Support or refute these generalizations, based on the evidence you collected. Explain your reasoning and provide evidence by include specific relevant numbers in your concluding statement, such that it can be read (and cited) on its own without referring to the above calculations and numbers. (Consider the uncertainty of your vertical motion parameters.)
Brief concluding statement:
 Bring up your whiteboards to the front of the class, to be presented to the instructor, which should include:
 A descriptive abstract: a brief summary of the purpose and methods used, but not of the data nor the conclusions. (Use the sample abstract below for today's lab.)
"We applied motion tracking software to analyze the vertical motion of an unassisted jump and wireassisted jump to separately test their realworld plausibility in a recreation of Kobe Bryant's Nike Hyperdunk commercial." Stepbystep procedure.
 Data table, calculations and/or results.
 Evidencebased conclusion statement.
 Documentation Rubric (tasks 12)
(Graded from randomly selected group member)
Score  Description 
3  Explanations complete and calculations correct, or very nearly so. 
2  Essentially complete; few explanations/calculations missing or incorrect. 
1  Substandard effort; substantive amount of explanations/calculations missing or incorrect. 
0  Unacceptable or no significant effort. 
 Whiteboard Rubric (task 3)
(Graded as a group, evaluated by instructor during debrief session)
Score  Description 
3  Complete, thorough, understandable, with little or no clarification needed during verbal instructor critique (can be resubmitted and presented again with requested corrections/revisions made, and still receive full credit). 
2  Minor problems; some corrections/revisions requested by instructor still needed, but not completed during time remaining in lab. 
1  Minimally acceptable effort, essential/critical revisions still needed. 
0  Unacceptable or no significant effort beyond experimental work. 
Followup
Complete this week's postlab assignment, next week's prelab assignment, and review lab instructions.
Due 12:00 PM before start of next lab
Postlab assignment 3 (*.html), 1 point
