Projectile motion
Projectile motion is motion in two dimensions under the
influence of a constant force. An object moving through the air near the
surface of the earth is subject to the constant gravitational acceleration g,
directed downward. If no other forces are acting on the object, i.e. if
the object does not have a propulsion system and we neglect air resistance, then
the motion of the object is projectile motion.
In this lab you will analyze the motion of a ball executing projectile motion.
Open a Microsoft Word document to keep a log of your
experimental procedures and your results. This log will form the basis of
your lab report. Address the points highlighted in blue.
Answer all questions.
Exercise
The New York Giants are tied with the Chicago Bears with only a few
seconds left in the game. The Giants have the football and call the
place kicker into the game. He must kick the ball 52 yards (47.5 m)
for a field goal.
If the crossbar of the goal is 10 ft (3.05 m) high,
and the maximum speed with which the kicker can kick the ball is 25 m/s,
which range of angles (in deg) will allow him to score the field goal?
Solve this problem using a spreadsheet. Produce a spreadsheet with
5 columns.
v_{0} (m/s) 
Angle (deg) 
t (s) 
x (m) 
y(m) 
Hint: Download this spreadsheet
to get started.
The first two columns each contain one entry each. Construct your
spreadsheet so that when you change these numbers, the numbers in the next
three columns will be updated. The time steps in the t(s) column
should be on the order of 0.1 s or smaller. The entries in the x(m) and y(m)
columns are calculated as a function of time using the
kinematic equations.
In one full sentence answer the question above.
Experiment
A ball is moving in two dimensions under the influence of a constant
gravitational force.
It is hard to get detailed information about its motion without using external
measuring instruments. In this experiment the instrument is a video
camera. You will analyze a video clip. The clip shows a ball being
thrown. You will determine the position of the ball in two
dimensions as a function of time by stepping through the video clip
framebyframe and by reading the time and the position coordinates of the ball
off each frame. You will construct a spreadsheet with columns for time and
position and use this spreadsheet to find the x and y component of the velocity
as a function of time.
Procedure:
To play the video clip or to step through it framebyframe click the "Begin"
button.
 "Play" the video clip. When finished, "Step up" to frame 1.
 In the setup window choose to track both
coordinate of the object.
 Click "Calibrate".
 Click "Calibrate X".
The video clip contains
two meter sticks. Position the cursor over left end of the horizontal stick and click the left mouse button. Then position the cursor
over the right end of the horizontal stick and click the left
mouse button again. This will record the ycoordinates of the chosen
positions. Enter the distance between those positions into the text box in
units of meter. For the example positions, you would enter 1 into the
text box. Click "Done".
Make sure the video frame stays fixed in the browser window between the two
clicks. You may have to scroll after the clicks to get to the buttons.
 Now click "Calibrate Y".
Position the cursor over bottom end of the vertical stick and click the left
mouse button. Then position the cursor over the top end of the vertical
stick and click the left mouse button again. This will record the
ycoordinates of the chosen positions. Enter the distance between those
positions into the text box in units of meter. For the example positions,
you would enter 1 into the text box. Click "Done".
Make sure the video frame stays fixed in the browser window between the two
clicks.
 Click the button "Click when done calibrating". A spreadsheet
will open up. Click "Start taking data".
 Start tracking the ball. Position the cursor over the
ball. When you click the left mouse button, the time and the x and ycoordinates
of the ball will be entered into the spreadsheet. You will automatically
step to the next frame of the video clip. Make sure the video frame stays
fixed in the browser window while you take data. When the ball is caught, click "Stop Taking
Data".
 Your table will have 3 columns, time (s), x( m), and y (m).
 Open Microsoft Excel, and paste the table into an Excel spreadsheet.
Produce graphs of the x and y components of position versus time.
Label the axes.
 Describe the graphs? Does one of the graphs resemble a
straight line? If yes, what does this tell you?
 Rightclick your data in the x(m) versus time graph and choose
"Add Trendline". Choose "Type, Linear" and "Options, Display equation on
chart". An equation y = ax + b will appear on your graph, where the
number a is the slope and the number b is the yintercept. What is
the physical meaning of the slope of this graph?
 Rightclick the data in your y(m) versus time graph and choose "Add
Trendline". Choose Polynomial, Order 2 and under options click "Display equation on
chart". An equation of the form y = b_{1}x^{2} + b_{2}
x + b_{3} will be displayed where b_{1}, b_{2}, and
b_{3} are numbers. What do the
coefficients b_{1} and b_{2} tell you?
 We can view the motion of a projectile as a superposition of two
independent motions. Describe those two motions.
Paste your graphs with trendlines into your log.
Activity
In this virtual laboratory you will investigate projectile
motion with and without air resistance. You will find the maximum range of
a baseball with given initial velocity and the launch angles required for it to
hit a target.
Procedure:
Open the
Projectile
Motion simulation. Click "Intro".
Position the canon 20 m to the left of the target. Make sure the cross
on the canon is at the same height as the target. Choose the baseball
projectile and give it an initial speed of 20 m/s.

(a) Given this initial speed there are two launch
angles for the baseball to hit the center of the target.
What is the smaller of these launch angles (within ~±1^{o})?
Note: You may have to raise the canon by 1 meter to get to the small
angle. Since you cannot raise the target, maye you can use the ruler to mark
where the target would be if it also was raised by 1 m. That should let you find
the small angle.
 (b) Given this initial speed there are two launch angles
for the baseball to hit the center of the target.
What is the larger of these launch angles (within ~±1^{o})?
 (c) Find the maximum range of the
projectile along the horizontal. For this maximum range note the launch angle and the hang
time of the baseball and estimate the maximum height of the baseball
above the ground during its flight.
Do this twice, once neglecting air resistance and once
with air
resistance with a drag coefficient of 0.35.
Fill in the table below. Compare your results with and without air
resistance. Paste your table into your log.
Projectile speed: 20 m/s 

Maximum range 
Launch angle (deg) 
Maximum height (m) 
Hang time (s) 
no air resistance 




drag coefficient 0.35 




Convert your log into a lab report.
Name:
Email address:
Laboratory 3 Report
 In one or two sentences state the goal of this lab.
 Insert your log with the requested graphs and the answers to the
questions in blue font.
Save your Word document (your name_lab3.docx), go to Canvas, Assignments, Lab
3, and submit your document.