Ready, Aim, Fire!
Are You on Target?
If you take the time to stop and think about it, parabolas are everywhere; in lighting, sound
waves, trajectories, architecture, art and…well, you get the picture. But do you really think
they have applications in real life, or are math teachers just pulling your leg to get you to
learn yet another useless fact? After this task, you just may realize the impact quadraticsavvyness has on the world (or if nothing else you will have completed a pretty cool project)!
You and your partners are going to build a catapult that launches mini-marshmallows. Do
you think you have what it takes to hit the mark…time and time again? Let’s find out!
Here’s what you need to do to get started:
Day 1
1. (Do this individually.) Go to Mrs. Edwards’ sharepoint site. On the top right side of
the page is a link called “Quadratic Equations.” Click on it, read it, and make a list of
10 facts (in complete sentences) from this article.
2. You will be placed in teams of 3. Each person in your team of 3 needs to research the
design of catapults (type the words catapult and design in an internet search engine).
Make/print sketches of a small tabletop catapult for your team. Keep in mind the
following supplies you will be given:
a. Popsicle
d. Pencils
h. Plastic
sticks
e. Glue
silverware
b. Rubber bands
f. Bottle tops
c. Paper clips
g. String
3. You may use additional materials from home if you choose. You will have one class
period to design your catapult.
**You are not building the catapult today. You are simply doing the research
with your team so that you are prepared to build the catapult next class period.
Day 2
1. Build your catapult. You must exercise maturity and good judgment during
construction and throughout the project. If you are caught launching anything from
your catapults at others or randomly in the classroom, your group will receive a ZERO
for this project!
2. You may use your own materials and those given to you in class. During construction
all team members must participate equally.
3. Catapult Guidelines:
1. Your catapult may not be larger than a ½1/2 sheet of paper.
2. Your catapult must launch a mini marshmallow at least 12 inches
horizontally.
3. You must be able to launch your marshmallow from the same spot
every time.
Day 3
1. Today your team needs to determine the equation for the path your marshmallow
follows. In order to complete this task, you must be very consistent with your catapult
launching. You will need 2 pieces of information:
a. The exact amount of time your marshmallow is in the air.
b. The exact distance the marshmallow travels.
2. Assign a timer, a recorder, and a launcher for this task. It will work better if the same
person completes the same task every time for this part. Record who is completing
what task on your worksheet.
3. Make a table of data on your worksheet that includes the trial number, time in air, and
distance traveled. Complete 25 trials (do at least 5 practice runs before you start
recording your data). Distance traveled does not include if the marshmallow slides or
rolls on the table once it has landed. Do not start the stopwatch until the marshmallow
has left the catapult arm.
4. When done, find the mean of the hang time (time in air) for your marshmallow.
Record this on your worksheet.

5. You will be using the equation for vertical motion to find the equation your parabola
makes. This formula can be found in your textbook throughout chapter 10 and is
2
h  16t  vt  c . So what does that mean?
a. h represents the height, in feet, of your object at any given time, t.
b. t represents time in seconds
c. v represents the velocity of your marshmallow when it leaves the catapult.
d. c represents the initial height of your marshmallow right before it launches from
the catapult.
Whew! That’s a lot of information, but take the time to become familiar with this
equation
and all it’s parts. It is what will make your launch accurate!
6. Because c represents the height at take-off, you will need to accurately measure the
height of your catapult launching arm when it is fully extended vertically. Make sure
your measurement is in feet, and record this value on your worksheet. (Have your
teacher check this answer.)
7. You will also need to know what h is in the equation. So let’s think. Your time was
measured until the marshmallow hit the ground/table. What is the height at that time?
Fill it in on your worksheet (Have your teacher check this answer.)
8. Fill in t (the average you found of all your trials) on your paper, and now you are ready
to find the equation for the parabola your marshmallow makes. Fill in the known
variables in your equation to solve for velocity. Once you have found velocity, fill it
in on your worksheet. (Have your teacher check this answer.)
9. Almost there! Now we can write the formula for your parabola knowing c, h, and v.
Fill these variables in the original equation, h  16t 2  vt  c . Use this equation to find
the vertex of your parabola. Fill in the vertex on your worksheet. What does this
vertex represent? (Have your teacher check this answer.)
10. Using your vertex information, place
 a target in the path of your marshmallow so that
the marshmallow will hit the bull’s-eye. (Be very still while holding the target!)
Launch your marshmallow. Does it hit the target? If not, you need to consider what
might be wrong with your equation. Tweek, remeasure, get it right! Your final task
will be to show your teacher your vertex, place a target at that spot, and hit the target
with your marshmallow.
Good Luck!
Parabolas and Catapults Worksheet
Timer:
_____________________
Recorder:
Launcher:
_____________________
_____________________
Mean Hang Time:
_____________________
Starting height, c, in feet: _____________________
Teacher Checked:
Height, h, at ending time: _____________________
Teacher Checked:
Time in air, t, of marshmallow: _____________________
Teacher Checked:
Vertical motion formula with c, h, and t plugged in and solving for v:
Velocity of marshmallow, v: _____________________ Teacher Checked:
Vertical motion formula with h, v, and c plugged in to find vertex:
Vertex of path of marshmallow: _____________________
What do each of the coordinates of the vertex represent?
Marshmallow Target Teacher Checked:
Teacher Checked: