Name:_________________________________ Lab Section: _________ Group Number: __________
Lab Partners: _______________________________________________ Grade:____________
Physics 201
Lab 3
Projectile Motion
Pre-Lab
Pre-lab Questions (turn in at start of lab)
For this lab, you will be using a spring-loaded launcher to fire a steel ball. The launcher can be adjusted to change
the launch angle of the projectile. In some instances, you may change the initial height of the launcher.
Pretend you have two launchers at the same height, side-by-side. One fires a projectile with a large initial velocity
and the other fires it with a small initial velocity. Both launchers fire horizontally.
1) If you fire the launchers at the same time, which projectile should land first? Briefly explain why.
2) Which one should go farther? Briefly explain why.
3) If the initial velocities are made to be the same, but one of the launchers is at a different height, which one
lands first (the projectile from the taller or shorter launcher)? Which projectile goes farther? Briefly
explain why.
4) Therefore, for the firing the ball horizontally, how do you maximize the time-of-flight? Note you can only
change the height of the launcher and the initial velocity. Should each of these be big or small, or does it
matter? By maximizing the time-of-flight, do you also maximize the distance?
5) For a single launcher, if you can change the angle of launch (0 to 90 degrees), but cannot change the initial
velocity how do you maximize time-of-flight? Does this correspond to maximizing the distance from the
launcher? Why or why not?
6) If you can change the angle of launch but not the initial velocity, what angle maximizes the distance of the
projectile? Give an intuitive answer (i.e. simple reasoning but no equations). Now, find or derive an
equation to support your answer.
Name:_________________________________ Lab Section: _________ Group Number: __________
Lab Partners: _______________________________________________ Grade:____________
Physics 201
Lab 3
Projectile Motion
Introduction The physical concepts explored in this lab are the same as those that govern the placement of a wellkicked punt, the trajectory of a charged particle in a uniform electric field, the best angle at which to throw a shotput, and the parameters needed to sink an enemy ship with a salvo. Needless to say, a thorough understanding
projectile motion affords the physicist and engineer powerful knowledge beyond the classroom and lab. In this
experiment, you will be building upon work in Lab 2: Motion of a Falling Body. Previously you were only
concerned about the motion of an object in one coordinate, the y-coordinate. In the following experiments you will
be exploring the motion of a projectile in two-dimensions, and using what you know to hit a target placed arbitrarily
on the floor (but within range) by your partner. The difficulty in the derivations, calculations, and understanding of
this material will be realizing how horizontal and vertical motion are coupled.
Procedure You will be using a projectile launcher which can fire a steel ball at a desired angle, and with three
different muzzle velocities. CAUTION: You must wear safety goggles at all times and should never look into the
barrel of the launcher!!!. You can check to see if the ball is loaded and determine the range setting by a yellow tab
seen through the slits in the top of the launcher. The position of the yellow tab indicates the muzzle velocity: short
range, medium range, and long range. Use the provided ramrod to cock the ball in the launcher (your fingers won’t
do much good). For the various experiments you will be using one or more of the following variables: initial
velocity, time, horizontal displacement, vertical displacement, and initial angle to either hit targets on the floor, or
make predictions about the trajectory of the projectile.
A plumb bob is provided to indicate the initial position in the x-coordinate, xo, on the floor. To find your xo, hang the
plumb bob from the initial position of the ball as it leaves the launcher and mark down the location on the floor
where the bob indicates. The initial angle of trajectory can be read off the launcher, and a tape measure and
stopwatch are provided for you to make additional measurements. Carbon paper will also be used to help you locate
the precise location of projectile when it hits the floor or another intended surface.
Here are a set of equations for projectile motion that you will be using to derive more interesting quantities. Note
that initial velocities in the x- and y- directions are given by vox  cos  and voy  sin respectively where  is the
initial angle of launch. Also, xo and yo represent the initial x and y-displacements.
Equations of Motion in y-coordinate
Equations of Motion in x-coordinate
ay t    g
ax  t   0
v y  t    gt  voy
v x  t   vox
1
y  t    gt 2  voy t  yo
2
x  t   vox t  xo
g  9.8 m s 2
From the list of equations above, we can solve for the time it takes for a projectile to get to the peak of its trajectory
as
𝑣𝑜𝑦
𝑡𝑝𝑒𝑎𝑘 =
𝑔
.
(1)
The corresponding peak height is
𝑦𝑝𝑒𝑎𝑘 =
2
𝑣𝑜𝑦
2𝑔
.
(2)
The entire time-of-flight it takes for the projectile to come back down to the same height from which it started is
𝑡𝑇𝑂𝐹 =
2𝑣𝑜𝑦
𝑔
.
(3)
Finally, the displacement in the horizontal direction of the projectile
𝑥=
𝑣𝑜2 𝑠𝑖𝑛2𝜃
𝑔
+ 𝑥𝑜 .
(4)
Calibration: Before predicting trajectories of projectiles and hitting targets on the floor, you will need to know the
muzzle velocity of the launcher. Pick one of the ranges on the launcher and stick with it for the rest of the
experiment
1) There are a number of ways to determine the muzzle velocity; can you think of two? Be creative but not
ridiculous. Given the tools we would likely have at Augustana or even a small budget of ~$1k, how would
you determine the muzzle velocity? There are many right answers, don’t spend too long on this.
In this lab, you will be calculating the muzzle velocity by firing the launcher in the horizontal position and
measuring displacements, and/or the time of flight. For a horizontal launch, we have no initial velocity in the ydirection, so all initial velocity is given to the x-coordinate. Therefore the total time of flight is simply
t  x vox  x vo and the initial velocity is simply vo  x t . However, we can get rid of the time variable
altogether by using what we know about the y-coordinate. Since there is no initial y-velocity, and the ball ends up at
zero height, yo  1 2 gt 2 . Solving for t, we get t 
g
2 yo
, so that vo  x t  x
g
2 yo
2) As you cans see, to find the initial velocity, you can fire the launcher and either measure x and t and use the
equation vo  x t , or you or you can fire the launcher and measure x and yo and use
vo  x t  x
g
.Which one is less error-prone experimentally? Why?
2 yo
After deciding the best method, fire the launcher at least eight times and take an average of the calculated initial
velocities. Measure x-distances by taping a piece of carbon paper to the floor with a piece of paper underneath. Use
an acoustic tile as a backstop propped against a chair unless you want to be chasing balls all over the room. Be sure
to calculate the standard deviation,  v , of the velocities using Excel. The standard deviation represents the likely
deviation of any future shot from the average position due to random error in your setup and measurement. It is
related to the error in the average value of velocity called the standard deviation of the mean, vave   v N .,
where N is the number of data points you measured. Quote your value using the following notation, vave  vave .
Experiment: Put the launcher on the floor. Have your partner pick any place on the floor in a direct line of the
trajectory < 2.5 meters away. Measure the intended distance x of the target, and calculate the angle needed in order
to hit this target Adjust the height of the lab jack to the same height as the ball within the launcher and place it at
the target position. Again, tape a piece of carbon paper to the surface of the lab-jack with a blank sheet underneath
in order to mark hits. Fire three times and record your results.
1) Were you close? Take your best value and calculate the difference you were off from the expected value as
well as the percent error.
2) The manufacturer claims the initial velocity will vary as much as 8% for minimum to maximum angles of
launch. If this is true, what range of values do you expect? Does your data fall within this tolerance?
3) Subtract your calculated angle from 90 degrees. Launch the ball another three times at this angle. What do
you find? What should happen if you compared a ball launched at 60 degrees and another at 30 degrees?
Explain in words the relative sizes of the initial velocities in the x-, and y-directions as well as the time of
flight in these two cases.
Now switch roles and repeat the above experiment. If there are three people in your group, you just need to one
additional target (two targets total).
4) From equation 4, you can find the angle for which the launcher gives maximum horizontal distance. Find
this angle and write down any work you used to calculate it in the space below. Set the launcher to this
angle and fire at least eight times. Does the average distance match your predicted distance? Be sure to also
quote the standard deviation of the mean and percent error.
Post-lab Questions:
1) What was the objective of this lab? Do you feel the objective was appropriately achieved? Why or why
not?
2)
Name the two most significant sources of error in this experiment (Be specific – do NOT say, for example,
“human error” or “equipment limitations”). Are these errors likely to be random or systematic? Explain.
3) Describe some ways that the error in this lab could be reduced, including the possible purchase of
additional equipment.
4) Why not use the plastic ball you saw fired in class? Would you expect better results or worse?
5) What if the ball did not land at the same height as the launch; what if you launched it at an angle from the
table and let it hit the floor? Would the ball travel farther or shorter than the case you did in lab? Why?
6) Finally, derive equations 1-4. Attach additional sheets of paper if needed.