HPP A8
The Jumping Human: Projectile Motion
Our goal in this activity is to use what we've learned for one dimensional motion, to help us
understand the motion of humans when airborne, such as divers, pole-vaulters, and jumping
ballet dancers.
Exploration
View the movie file StandingLJ60256x240.mov. You'll find it on BlackBoard in
Resources>Movies. Note carefully the motion of the jumper. Concisely describe the jumper's
motion as completely as you can. Is the motion smooth? Is there any acceleration? How many
coordinates do you need to describe the motion?
GE 1. Jumping vertically
If it is not already set up, mount the motion detector from the overhead metal
frame. Make sure the motion detector is looking straight down. Load the
DataStudio file distance.ds. Stand directly under the motion detector, start the
data acquisition, and jump as high as you can (don't hit the motion detector!).
Keep your hands at your side and your legs straight while in the air. Make sure
you get a "good" data set. Show your graph to your instructor.
1. Looking carefully at your best graph, determine, a) where your feet left the
floor, b) where you were at the highest point, and c) where your feet first
touched the floor again on the way down. If you're not sure, ask your
instructor.
2. While you were in the air (not touching the floor) was your velocity ever
zero? At what time? No fare peaking at the velocity graph yet!
3. At what position was the velocity zero? Again, only consider the motion
while your feet were not touching the floor.
4. Looking only at the position vs. time graph, was there ever non-zero
acceleration? How do you know?
Activity Guide
 2010 The Humanized Physics Project
Supported in part by NSF-CCLI Program under grants DUE #00-88712 and DUE #00-88780
HPP A8
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5. Having collected the position data and observed the motion, predict if the
acceleration is ever zero. Again, only consider the motion while the feet are
off the floor.
6. Looking only at the position vs. time graph, can you tell if there was ever
non-zero acceleration? If so, at what time or position? How do you know?
7. Describe the velocity vs. time graph while the feet are not touching the
floor. Is the slope constant? Positive or negative?
8. Return to your data in DataStudio and display the velocity vs. time graph.
How good was your prediction in question 3?
9. Now, looking at the velocity vs. time graph, are you confident that your
prediction in question 5 is correct?
10. Return to the your data in DataStudio and display the acceleration vs. time
graph. Describe the acceleration graph while both feet are in the air.
11. Looking at the acceleration vs. time graph, how good was your prediction
in question 5?
12. What is the mathematical function that best describes your velocity data?
What is the value of the acceleration in this case?
Invention
Let us look at a simpler case than the standing long jumper and learn to collect data from digital
video clips. Execute the following steps carefully:
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Download the movie shaq.mov from the Movie folder in the Blackboard Resources
page.
Open the program called VideoPoint and close the opening splash screen titled "About
VideoPoint".
Activity Guide
 2010 The Humanized Physics Project
HPP A8
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Select "Open Movie" and then locate and open the movie shaq.mov.
You are going to follow the motion of 1 object - a basketball.
Select "Ok" to begin data analysis
GE 2.
1. A digital movie, like this one, is a series of still images called frames that
are taken at very precise time intervals. For this movie there are 30 frames
every second. How much time elapses between any two frames? Show your
work.
2. Digital images are composed of a regular grid of very small elements called
pixels. To collect useful data from the images you must create a scale. In this
movie, there is a board in the opening frame. How tall is the board in meters?
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You can use the known height of the board to create the scale. VideoPoint
will help with this process. Click on the "Ruler" icon on the left side of the
screen. A popup screen titled "Scale Movie" will appear.
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Enter the length you calculated in step 7 and click on the continue button.
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Click on one end of the board and then the other. VideoPoint now knows
how many pixels there are in each meter of distance.
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Play the movie using the controls at the bottom of the movie. You can
drag the slider with the mouse, click on the step buttons at the lower right
hand side of the screen, or use the keyboard arrow keys to step through the
movie one frame at a time.
3. Describe the motion of the basketball. Compare the motion of the
basketball to the motion of the standing long jumper.
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Now you are ready to collect data. Advance the movie until the basketball
just leaves the hands of the shooter. You should have a round cursor on the
movie window that says "Point S1" beside it. Now click on the basketball
and the movie will advance by one frame and position data will be
recorded in a table. Continue clicking on the basketball until just before it
goes into the hoop.
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Now click on the "Table" icon just below the "Ruler" icon on the left-hand
side of the VideoPoint screen. A table of your data should appear with a
time column, an x-position column, and a y-position column. These are
the "numbers" that form the basis of a mathematical model. Next you will
graph your data….
Activity Guide
 2010 The Humanized Physics Project
HPP A8
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Click on the "Graph" icon at the right hand side of the screen just under the
"Table" icon. A new window titled "Plot Series" will appear. Select time as
the horizontal axis and Point S1 y position as the vertical axis. Click "Ok" and
you should now have a graphical form of your data.
4. Does this graph look similar to anything you've done so far? Describe your
new graph. Does it indicate constant velocity?
Click on the "Graph" icon again and this time select "Time" as the horizontal
axis and Point S1 x position as the vertical axis. Select "Ok". Describe the
resulting graph.
5. Does it describe constant velocity? Does this graph resemble other graphs
you've made?
Click on the "F" icon in the upper right hand side of the "x-pos vs. time"
graph. Select "Linear" as the type of fit and then ok.
6. Does the resulting line closely approximate the data? If so, write the
equation of the best-fit line in the space below. Remember, it should have the
form x = m*t+x0.
7. What about the y-pos data? Can you produce a more helpful graph to help
model the motion? Create another graph by clicking on the "Graph" icon and
select "time" for the horizontal axis again and "Point S1" y position for the
vertical axis. Click "Ok" and describe this new graph. Is it linear? What does it
indicate to you based on your simple motion model already developed?
8. Click on the "F" icon in the "y-vel vs. time" graph and select "Linear" for
the type of fit and then "Ok". How well does this best-fit line describe the yvel vs. time data? Record the equation of the best-fit line in the space below.
Remember, it should have the form vy=m*a+v0.
9. Based on the graphs and functional representations of your data, describe
how a simple object like a basketball moves through the air.
We call this motion, projectile motion. It was first used by Galileo to predict how far a projectile
(such as a cannon ball) would travel. It can be described as two distinct and independent
motions: 1) Constant velocity in the x-direction and 2) Constant acceleration in the y-direction.
Activity Guide
 2010 The Humanized Physics Project
HPP A8
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Near the surface of the Earth the accepted value of that constant acceleration is -9.8 m/s (it is
directed down toward the center of the Earth).
The appropriate equations that describe projectile motion are:
x  v x 0t  x0
and
y  12 at 2  vy 0 t  y0 and
v y  ay 0 t  v y0
GE 3.
1. Now compare the motion of the basketball to the motion of the standing
long jumper. Are they exactly the same? Is any part of the motion the same? Is
the motion of the standing long jumper projectile motion? Explain.
Application
Let's go back and look at the standing long jump. Is the motion of the jumper like that of the
basketball? Do the legs and arms play a role in the motion?
1. Open VideoPoint if it isn't already open.
2. Open the movie StandingLJ60256x240.mov and note that you will follow one object.
3. Using the ruler, tell VideoPoint the length of a known object (look at the second frame).
4. Step the movie forward until the jumper's feet just leave the ground.
5. Begin clicking (taking position data) on the bright cross at the jumper's waist.
6. Continue until the jumper's feet are just above the floor again (but not touching!).
GE 4.
1. Graph x-pos vs. time. Describe this graph in the space below. Is this what
you would expect for projectile motion?
2. Graph y-pos vs. time. Describe this graph in the space below. Is this what
you would expect for projectile motion?
3. Graph y-vel vs. time. Describe this graph in the space below. Is this what
you would expect for projectile motion?
Activity Guide
 2010 The Humanized Physics Project
HPP A8
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4. Does bending the legs affect the motion? Go back to DataStudio and take
one more set of data. When you first collected your jumping up data you were
instructed to keep your legs straight and your arms at your side while you
jumped. Now jump up and lift your legs like the long jumper did. How well
does the bent-legs data compare to the straight-legs data?
5. In words, describe what it means for an object or body to be undergoing
"projectile motion." Be as detailed as possible in your description.
Activity Guide
 2010 The Humanized Physics Project