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Students Builds and Launches Rockets in
Upward Bound’s Pre-Calculus Class
This past summer, 2007, in the Upward Bound Program, at Georgia State University, Students in Mr. Duncan’s Pre- Calculus
Class, put their Calculus skills together in the designing, building and launching of their High Flying Rockets.  The summer class
began with the students forming Rocket teams of four to learn Pre-Calculus.  Monday, Wednesdays, and Thursdays were used to
learn the principles of Calculus.  Fridays was used to build their rockets.  The students studied and learned the principles involved
in the Cartesian Plane and Functions.  The Mission of the Rocket Project was to use the Position and Velocity Functions for free
falling objects to calculate the maximum height and initial velocity of their Rocket.  Listed below is the Position and Velocity
Functions and the terms contained in each function.  The most important scientific data the students measured for their rocket
experiment is the time from the rocket is launched into space to when the rocket reaches its maximum height and starts to return to
the earth.  

Position Function:        S(t) = -1/2gt2 + Vot + So     or    S(t) = -16t2 + Vot + So                           

Velocity Function:   V(t) = -32t + Vo

Where:          S(t) = Height of the Rocket at any time “t”.                                                               
V(t) = Velocity of Rocket at any time “t”
g = the Acceleration of Gravity (a constant)                                                      
g = -9.8m/s2 or -32ft/s2                                                                                      
t = time in seconds                                                                                        
Vo = the Initial Velocity of the object                                                            
So = the Initial Position of the object

The materials the students used to build their High Flying Rockets included two-liter plastic soda bottles for the rockets fuci loge ,
oak tag paper to give their rocket color, duck tape to hold the rocket together, and 1/8 inch thick plastic sheet for the rocket wings.  
The students first constructed the Fuci loge for their rocket, after they designed their wings, and attached the wings to the fuci loge
using a hot glue gun.  Next, the students designed and constructed the Nose Cone for their rocket.  The nose cone was
constructed using oak tag paper, liquid nail, duck tape, and clear plastic tape.  The design of the nose cone was the most
important part of the construction of the rocket because in order for there to be a perfect launch and the parachute to work properly,
the nose cone had to be built to specification.  Next the students constructed their parachute using eights pieces of string and thin
plastic cut into the shape of an octagon.  The students weren’t able to build the Launch Pad used to launch the rockets because of
the short time involved in the summer program, but they were ready to stay longer and learn more calculus if they were able to
continue with the building the launch pad.   
After building their rockets, the student teams were ready to launch their rockets and conduct their experiment.  Each team was
bragging and boasting about their rocket, saying, “my rocket is going to fly the highest, fastest”, and that they will have a perfect
flight.  Students used the stop watch feature on their cell phones to measure the time of upward flight of their rockets.  The High
Flying Rockets use compressed air and water (H2O as rocket fuel) to launch their rockets.  There is no fire or spark needed to
launch the High Flying Rockets.  There is still danger involved in using the High Flying Rockets because anything under high
pressure could explode.  Therefore safety was the most important concern in using the High Flying Rockets.  Safety glasses and
no kid playing was the rule on launch day.  The students had fun launching their rockets and watching them return safely to the
earth by means of its parachute.  There was a glow of amazement, happiness, and fascination from the students and on lookers to
see the results of their creation.  Not all launches were successful because on a couple flights, the nose cone did not separate
from the rocket after it reached its maximum height, therefore the parachute did not deploy.  The student’s interest in Mathematics
and Science was sparked by having fun using their High Flying Rocket and demonstrating the principles of calculus they learned in
a real life activity.  “This made learning math fun”, many said.  Students were inspired and ready to learn more about how our world
works.
After recording the data of their rocket launch, the students were ready to complete their lab project.  This included their lab write up,
in which they had to use the position and velocity functions to calculate the maximum height their rockets flew and initial launch
velocity that their rocket took off at.  The experiment was conducted at two different launch pressures, 60lbs. and 70lbs.  In the lab
write up, students had to answer the following question.  At what pressure did the rocket fly the highest and why?  What were some
of the factors that affected the maximum height your rocket traveled?  What did you discover about math and the real world from
building and launching your rocket?  What other moving vehicles can a rocket engine be used to power?  To the last question,
students suggested putting a rocket engine on a bicycle which now will be our aim in the Upward Bound Program for the summer
of 2008.
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