Visual Physics 218 – Projectile Motion [Lab 2]
In this experiment, you will be using your video equipment to evaluate two-dimensional motion.
It will be necessary to plot the data in an xy-coordinate system and separate the data into x and
y components. These components will be used to calculate parameters describing projectile
motion, including angle, initial velocity, range, and time. You should be able to identify the
random and systematic errors associated with your analysis and the cumulative effect of these
errors. In addition, this lab will require analyzing video clips of actual football game footage to
determine these same parameters for the projectile motion of a football kick-off.
Pre-Lab
Read Chapter 3 from Young & Freedman’s University Physics. Study two-dimensional motion
and learn how to identify and plot displacement, velocity, and acceleration on a graph, such as
those graphs you created in Lab 0 and Lab 1. You need to understand how graphs of
displacement, velocity, and acceleration relate to each other in two dimensions and how to
incorporate different types of error into your analysis.
Questions to be answered in your lab journal:
1. Search the internet and write down, in your own words, the definition of a random error and a
systematic error.
2. In this experiment, you will be using the marble launcher to project the marble at different
angles and speeds. List what you think the sources of random errors will be in this experiment.
Also list what you think will be the sources of systematic errors in this experiment.
3. In Lab 1, Experiment 1 you were asked to plot a trendline for vertical motion. You will also be
plotting trendlines in this experiment as well. What type of trendline (i.e., linear (polynomial 1storder), quadratic (polynomial 2nd-order), exponential, logarithmic, etc.) should you use for
horizontal displacement and horizontal velocity, assuming air resistance is not negligible? What
type of trendline should you use for vertical displacement and vertical velocity?
NOTE: During the experiments in which a marble launcher is used, all students in the lab
room are required to wear safety glasses at all times. Failure to wear safety glasses will
mean expulsion from the lab and a grade of zero (with no makeup available). Safety
glasses are available at the front TA desk.
Experiment 1
In experiment 1, you will project marbles at three different angles using the same power setting
on the marble launcher. Try to get as much of the marble’s parabolic trajectory in the camera’s
field of view as possible, though it is not necessary to get the marble’s entire trajectory to
calculate your results. The more of the flight parabola of the marble you can get into the movie,
the more accurate your results will be that you will obtain off the movies. Even with only half of
the marbles trajectory in the movie, the results you obtain inserting trendlines will be reasonably
similar using different parameters. Make sure you note which angle goes with each video, in
case the angle of the launcher arm cannot be determined by viewing the video.
1
Procedure:
Visual Physics 218 – Projectile Motion [Lab 2]
1. Place the marble launcher and the white poster board on the end of the lab table as in
Lab 0 and Lab 1, Experiment 3. Mount the camera on the rod and stand and place it on
the lab table top. The camera should be aimed directly at the plane of the marble’s
trajectory. One of the lab partners should hold a meter stick in front of the poster board
so that the tick marks are clearly visible in the camera image.
2. The marble launcher has different angle settings from 0° to 90°. See Figure 1. This angle
will be the angle θ of the initial velocity vo. The angle can be changed by un-tightening
the large knob on the rear of the launcher arm of the marble launcher and rotating the
launcher arm to the appropriate angle, then retightening the knob. First, set the angle to
60°. Now set the power setting to the second lowest setting (#2 mark on the launcher).
Perform a few test shots to make sure the camera and marble launcher are positioned
properly. If possible, try to get as much of the flight parabola of the marble in the camera
field of view, though this is not essential. It is imperative though that you get at least the
first half and apex of the parabola. This will ensure accurate trendline equations. Capture
the trajectory to video.
3. Set the
angle to
75° and
repeat step
2.
4. Finally, set
the angle to
85° and
repeat step
2.
5. After all the
movies for
Lab 2 have
been
recorded
for all
experiments, remove the
Figure 1
memory card from the
camera and insert the card into the computer. Copy the movies to your section folder
under the C:\218Labs folder. Insert one of the three movies for Experiment 1 into a new
LoggerPro sheet.
6. Use the Set Scale function and select two tick-marks on the meter stick as your
distance. Next, use the Add Point function and select a point on the marble in every
frame such that you have data points for the marble’s entire trajectory that is in the
movie. Now Set Origin and drag the origin of your coordinate axes to the point where the
marble is resting in the launcher before the marble is launched. This should also be your
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Visual Physics 218 – Projectile Motion [Lab 2]
first point selected. Your second point selected should be the first frame where the
marble is in flight. Your LoggerPro sheet should look similar to Figure 2. Export your
data to a text file and save the text file in your section folder. Remember to either save
this text file to a USB flash drive or email this text file to yourself when you are finished
with the lab.
7. Repeat step 6. for the remaining two movies.
Questions to be answered in your Technical Memo:
1. Open up the text file in an Excel sheet. You are going to find the horizontal and vertical
components of the initial velocity and acceleration by two different methods. First, plot a chart of
Vx vs. t. Now add a trendline and select Linear and Display Equation on chart. The equation
displayed on the chart will be in the general form y = bx + c, where b and c are the constant
coefficients. For constant acceleration, recall the kinematical equation of motion vx = axt + vox,
where a is the acceleration. Now compare these two equations and you see b = ax and c = vox.
From this you can determine vox and the horizontal acceleration ax. The horizontal acceleration
ax ≠ 0 since there is a small amount of air resistance. Next, plot a chart of Vy vs. t, and find voy
and ay using the same procedure. Do this for all three movies and Copy and Paste your charts
into your TM. Figure 3 shows two example charts.
Figure 2
2. Now you are going to find these same parameters using the position versus time graphs. Plot
a chart of Y vs. t. Add a trendline and select Polynomial: Order 2 and Display Equation on chart.
The equation displayed on the chart is in the general form y = ex2 + fx + h, where e, f, and h are
the constant coefficients. Recall for constant acceleration the vertical kinematical equation of
motion y = ½ayt2 + voyt + yo. Compare these two equations and you see e = ½ay, f = voy, and
3
Visual Physics 218 – Projectile Motion [Lab 2]
h = yo. Since this is vertical motion, you know that ay = g, or g = 2e, where e is the constant
coefficient of the equation displayed on the chart and g is the acceleration due to gravity. You
have also determined voy as well. Do this for all three movies and Copy and Paste your charts
into your TM. Figure 4 shows an example chart.
3. Plot a chart in Excel of the horizontal position versus time, or X vs. t. Add a trendline and
select Polynomial: Order 2 and Display Equation on chart. The equation displayed on the chart
will be in the general form y = jx2 + kx + n, where j, k, and n are the constant coefficients. Recall
for constant acceleration the horizontal equation of motion x = ½axt2 + voxt + xo. Compare these
two equations and see j = ½ax, k = vox, and n = xo. From this you have determined ax and vox. Do
this for all three movies and Copy and Paste your charts into your TM. Figure 4 shows an
example chart.
4. In your TM, compare your different values of vox, voy, ax, and ay using the two different
charting methods described above. Calculate the average vox, voy, ax, and ay.
Figure 3
4
Visual Physics 218 – Projectile Motion [Lab 2]
Figure 4
5. Now calculate the range and hang time of the marble. Do not obtain these values directly off
the movies, but calculate them using the averages of the two values of vox, voy, ax, and ay you
just computed. To do this, you will need the angle θ of each marble trajectory. To find the range
R, use the range formula:
𝑅=
𝑣𝑜2 sin 2𝜃
𝑔
Remember, this formula was derived using the condition y = yo, or Δy = 0. Thus, it is only
applicable for these specific conditions. Also recall that vo in this formula is the total initial
velocity calculated using the horizontal and vertical velocity components vox and voy:
voy
vo
θ
vox
𝑣𝑜 = �𝑣𝑜𝑥 2 + 𝑣𝑜𝑦 2
To calculate the hang time, recall the horizontal equation of motion x = ½axt2 + voxt + xo. You just
calculated the range, or total horizontal distance traveled, thus x = R. This gives the horizontal
equation of motion R = ½axt2 + voxt + xo. To find the hang time, solve this quadratic equation for t
and substitute in your average values of ax and vox, as well as xo, and compute t. This time t will
correspond to the point of maximum horizontal distance, or the time t at R. List the values of the
range and hang time you compute for all three marble shots at different angles in your TM.
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Visual Physics 218 – Projectile Motion [Lab 2]
Experiment 2
In Experiment 2, you will project marbles at three different power settings using the same angle
on the marble launcher. Try to get as much of the marble’s parabolic trajectory in the camera’s
field of view as possible, though it is not necessary to get the marble’s entire trajectory to
calculate your results. The more of the flight parabola of the marble you can get into the movie,
the more accurate your results will be that you will obtain off the movies. Even with only half of
the marbles trajectory in the movie, the results you obtain inserting trendlines will be reasonably
similar using different parameters. Make sure you note which power setting goes with each
video, in case the power setting of the launcher arm cannot be determined by viewing the video.
Procedure:
1. Set the marble launcher to the angle of 75°. This angle will be the angle θ of the initial
velocity vo. Leave the marble launcher at this angle θ for all of Experiment 2. The marble
launcher has different power settings. Set the power setting to the third lowest setting
(#3 mark on the launcher). Perform a few test shots to make sure the camera and
marble launcher are positioned properly. If possible, try to get as much of the flight
parabola of the marble in the camera field of view, though this is not essential. It is
imperative though that you get at least the first half and apex of the parabola. This will
ensure accurate trendline equations. Capture the trajectory to video.
2. Set the power setting to the second lowest setting (# 2 mark) and repeat step 1.
3. Finally, set the power setting to the lowest setting (# 1 mark) and repeat step 1.
4. After all the movies for Lab 2 have been recorded for all experiments, remove the
memory card from the camera and insert the card into the computer. Copy the movies to
your section folder under the C:\218Labs folder. Insert one of the three movies for
Experiment 2 into a new LoggerPro sheet.
5. Use the Set Scale function and select two tick-marks on the meter stick as your
distance. Next, use the Add Point function and select a point on the marble in every
frame such that you have data points for the marble’s entire trajectory that is in the
movie. Now Set Origin and drag the origin of your coordinate axes to the point where the
marble is resting in the launcher before the marble is launched. This should also be your
first point selected. Your second point selected should be the first frame where the
marble is in flight. Your LoggerPro sheet should look similar to Figure 2. Export your
data to a text file and save the text file in your section folder. Remember to either save
this text file to a USB flash drive or email this text file to yourself when you are finished
with the lab.
6. Repeat step 5. for the remaining two movies.
Questions to be answered in your Technical Memo:
1. Open up the text file in an Excel sheet. You are going to find the horizontal and vertical
components of the initial velocity and acceleration by two different methods. First, plot a chart of
Vx vs. t. Now add a trendline and select Linear and Display Equation on chart. The equation
displayed on the chart will be in the general form y = bx +c, where b and c are the constant
6
Visual Physics 218 – Projectile Motion [Lab 2]
coefficients. For constant acceleration, recall the kinematical equation of motion vx = axt + vox,
where a is the acceleration. Now compare these two equations and you see b = ax and c = vox.
From this you can determine vox and the horizontal acceleration ax. The horizontal acceleration
ax ≠ 0 since there is a small amount of air resistance. Next, plot a chart of Vy vs. t, and find voy
and ay using the same procedure. Do this for all three movies and Copy and Paste your charts
into your TM. Figure 3 shows two example charts.
2. Now you are going to find these same parameters using the position versus time graphs. Plot
a chart of Y vs. t. Add a trendline and select Polynomial: Order 2 and Display Equation on chart.
The equation displayed on the chart is in the general form y = ex2 + fx + h, where e, f, and h are
the constant coefficients. Recall for constant acceleration the vertical kinematical equation of
motion y = ½ayt2 + voyt + yo. Compare these two equations and you see e = ½ay, f = voy, and
h = yo. Since this is vertical motion, you know that ay = g, or g = 2e, where e is the constant
coefficient of the equation displayed on the chart and g is the acceleration due to gravity. You
have also determined voy as well. Do this for all three movies and Copy and Paste your charts
into your TM. Figure 4 shows an example chart.
3. Plot a chart in Excel of the horizontal position versus time, or X vs. t. Add a trendline and
select Polynomial: Order 2 and Display Equation on chart. The equation displayed on the chart
will be in the general form y = jx2 + kx + n, where j, k, and n are the constant coefficients. Recall
for constant acceleration the horizontal equation of motion x = ½axt2 + voxt + xo. Compare these
two equations and see j = ½ax, k = vox, and n = xo. From this you have determined ax and vox. Do
this for all three movies and Copy and Paste your charts into your TM. Figure 4 shows an
example chart.
4. In your TM, compare your different values of vox, voy, ax, and ay using the two different
charting methods described above. Calculate the average vox, voy, ax, and ay.
5. Now calculate the range and hang time of the marble. Do not obtain these values directly off
the movies, but calculate them using the averages of the two values of vox, voy, ax, and ay you
just computed. To do this, you will need the angle θ of the marble trajectory. To find the range
R, use the range formula:
𝑣𝑜2 sin 2𝜃
𝑅=
𝑔
Remember, this formula was derived using the condition y = yo, or Δy = 0. Thus, it is only
applicable for these specific conditions. Also recall that vo in this formula is the total initial
velocity calculated using the horizontal and vertical velocity components vox and voy:
voy
vo
θ
vox
𝑣𝑜 = �𝑣𝑜𝑥 2 + 𝑣𝑜𝑦 2
To calculate the hang time, recall the horizontal equation of motion x = ½axt2 + voxt + xo. You just
calculated the range, or total horizontal distance traveled, thus x = R. This gives the horizontal
7
Visual Physics 218 – Projectile Motion [Lab 2]
equation of motion R = ½axt2 + voxt + xo. To find the hang time, solve this quadratic equation for t
and substitute in your average values of ax and vox, as well as xo, and compute t. This time t will
correspond to the point of maximum horizontal distance, or the time t at R. List the values of the
range and hang time you compute for all three marble shots at different power settings in your
TM.
Experiment 3
In this experiment, you will be analyzing actual game video of a football game and plotting the
trajectory of a football during a kick-off. You do not need to see the entire flight of the football
during the kickoff, just enough to plot an accurate trendline of the parabola. There is no
equipment to set up for this experiment. The movies are already saved on your computers.
Procedure:
1. The three kick-off movies are in the C:\218Labs\Kickoff folder. Start LoggerPro and
insert one of the kick-off movies from this folder into a new LoggerPro sheet.
2. Use the Set Scale function and select two yard line markers on the football field as your
distance. These yard line markers are ten yards apart. If you want the data you will
calculate to be in meters, then you must convert yards to meters and enter the scale in
meters. Next, use the Add Point function and select a point on the football in every frame
such that you have data points for the football’s entire trajectory that is in the movie. Now
Set Origin and drag the origin of your coordinate axes to the point where the football is
resting on the tee before the football is kicked. This should also be your first point
selected. Your second point selected should be the first frame where the football is in
flight. Export your data to a text file and save the text file in your section folder.
Remember to either save this text file to a USB flash drive or email this text file to
yourself when you are finished with the lab.
3. Repeat steps 1. and 2. for the remaining two kick-off movies.
Questions to be answered in your Technical Memo:
1. Open up the text file in an Excel sheet. You are going to find the horizontal and vertical
components of the initial velocity and acceleration of the football by two different methods. First,
plot a chart of Vx vs. t. Now add a trendline and select Linear and Display Equation on chart.
The equation displayed on the chart will be in the general form y = bx +c, where b and c are the
constant coefficients. For constant acceleration, recall the kinematical equation of motion
vx = axt + vox, where a is the acceleration. Now compare these two equations and you see b = ax
and c = vox. From this you can determine vox and the horizontal acceleration ax. The horizontal
acceleration ax ≠ 0 since there is a large amount of air resistance on the football. Next, plot a
chart of Vy vs. t, and find voy and ay using the same procedure. Do this for all three kick-off
movies and Copy and Paste your charts into your TM.
2. Now you are going to find these same parameters using the position versus time graphs. Plot
a chart of Y vs. t. Add a trendline and select Polynomial: Order 2 and Display Equation on chart.
The equation displayed on the chart is in the general form y = ex2 + fx + h, where e, f, and h are
the constant coefficients. Recall for constant acceleration the vertical kinematical equation of
motion y = ½ayt2 + voyt + yo. Compare these two equations and you see e = ½ay, f = voy, and
8
Visual Physics 218 – Projectile Motion [Lab 2]
h = yo. Since this is vertical motion, you know that ay = g, or g = 2e, where e is the constant
coefficient of the equation displayed on the chart and g is the acceleration due to gravity. You
have also determined voy as well. Do this for all three kick-off movies and Copy and Paste your
charts into your TM.
3. Plot a chart in Excel of the horizontal position versus time, or X vs. t. Add a trendline and
select Polynomial: Order 2 and Display Equation on chart. The equation displayed on the chart
will be in the general form y = jx2 + kx + n, where j, k, and n are the constant coefficients. Recall
for constant acceleration the horizontal equation of motion x = ½axt2 + voxt + xo. Compare these
two equations and see j = ½ax, k = vox, and n = xo. From this you have determined ax and vox. Do
this for all three movies and Copy and Paste your charts into your TM.
4. In your TM, compare your different values of vox, voy, ax, and ay using the two different
charting methods described above. Calculate the average vox, voy, ax, and ay.
5. Now calculate the range and hang time of the football. Do not obtain these values directly off
the kick-off movies, but calculate them using the averages of the two values of vox, voy, ax, and
ay you just computed. To do this, you will need the angle θ of the football trajectory. To find the
angle, you can use the average initial velocity components you calculated. From the vector
diagram of the initial velocity, recall that the relation between the initial velocity and angle is:
voy
vo
θ
vox
tan 𝜃 =
𝑣𝑜𝑦
𝑣𝑜𝑥
Using this expression, you can solve for θ and calculate the angle of the initial velocity of the
football. To find the range R of the football, use the range formula:
𝑅=
𝑣𝑜2 sin 2𝜃
𝑔
Remember, this formula was derived using the condition y = yo, or Δy = 0. Thus, it is only
applicable for these specific conditions. Also recall that vo in this formula is the total initial
velocity calculated using the horizontal and vertical velocity components vox and voy:
𝑣𝑜 = �𝑣𝑜𝑥 2 + 𝑣𝑜𝑦 2
To calculate the hang time of the football for the entire kick-off, recall the horizontal equation of
motion x = ½axt2 + voxt + xo. You just calculated the range, or total horizontal distance traveled,
thus x = R. This gives the horizontal equation of motion R = ½axt2 + voxt + xo. To find the hang
time, solve this quadratic equation for t and substitute in your average values of ax, vox, and xo
and compute t. This time t will correspond to the point of maximum horizontal distance, or the
time t at R. List the values of the range and hang time you compute for all three kick-off movies
in your TM.
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Visual Physics 218 – Projectile Motion [Lab 2]
EQUIPMENT LIST FOR LAB 2:
Safety Goggles
Camera (memory card and AC charger)
Heavy duty stand with finger clamp
Launcher and marble
Poster board
Meter stick
THINGS TO DO AT THE END OF THE LAB SESSION:
1. Replace the heavy stand, rod, clamp on the lab table.
2. Replace the camera (with the LCD view finder window closed) on the shelf of the lab
table.
3. The meter stick should be put on the shelf of the lab table.
4. The memory card should be left in the slot in the computer monitor.
5. Leave the other items in neat order on the lab table. Be sure to leave the marble in the
launcher.
6. Put your safety goggles back in the box at the front TA table.
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