Addressing Standards with
Model Rocketry
Dr. Cwiakala
June 2003
Using skills learned in Exit
Exam Preparation Class,
Algebra-I & II, and PreCalculus, a rocket’s
maximum altitude is
determined
Outline of Presentation
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Objective
Background
Problem
Solution 1- Basic Skills
Solution 2 - Algebra-II
References & more
Objective
• Determine how high the rocket flew using:
- Basic Skills Approach - scale drawing
- Algebra-I & II Approach - linear equations
o Develop equations for lines
o Solve for intersection
o Automate using a spreadsheet
- Precalculus – Law of Sines and Trig Functions
Background
• Started in the late 50’s
due to interest in space
exploration.
• Model Rocket and
supplies can be
purchased from
department stores and
hobby shops.
Background: Equipment
• Rocket & Engines
• Launch Pad
• Launch System
• Tracking Device
Background: Rocket Flight
Background: Tracking Device
• Tracking device is
used to determine the
maximum angle the
rocket’s path makes
with respect to a
tracking location
Problem: Tracking
• Tracker follows
rocket’s flight path
• Records
maximum
angle
Solution 1: Graphical
Algebra Approach – Overview
(class per topic)
• Using the graphic approach, develop
equations for specific data – slope and
distance
• Develop literal equations for any slope and
distance
• Automate using a spreadsheet
• Perform experiment and collect data - FUN
• Enter data and determine results
Solution 2: Algebra-II Approach
Y=Ma(X-60)
Y=Mb(X+60)
Eq. 1: Line from tracking station A
Eq. 2: Line from tracking station B
Ma=tan(Aa)
Mb=tan(Ab)
Eq. 3: slope of tracking line A
Eq. 4: slope of tracking line B
Xmax=60(Mb-Ma)/(Mb+Ma)
Eq. 5: X location for
maximum altitude
Solution 2: Spreadsheet *
ROCKET ALTITUDE CALCULATIONS
Keenan High School
Dr. Cwiakala
NOTE: Input cell have blue borders
Formulas Used in the Rows
=TAN(Aa*PI()/180)
=D*(Mb-Ma)/(Mb+Ma)
=TAN(Ab*PI()/180)
=Ma*(Xab+D)
NOTE: TAN function requires angles in radians
Tracking Station
Distance from
Launch pad
Flight D
1
2
3
Angles in Degrees
Aa
Ab
60
48
37
60
38
35
60
40
45
Slopes from Angles
Position and Altitude
Ma
Mb
Xab
Yab
1.110613 0.7535541
-11.5
53.9
0.781286 0.7002075
-3.3
44.3
0.8391
1
5.2
54.8
Algebra II Standards Covered
• I-B1- Gather & record
data
• I-B2- Represent
relationships among
quantities using concrete
models … using
spreadsheets
• I-B3- Interpret situations
in terms of given graphs
and create situations that
fit given graphs
Algebra II Standards - Cont.
• I-F1- Recognize that real- • II-B2- Solve systems
of linear equations
world phenomena can be
using concrete
modeled by specific
models, graphs,
functions
tables, and algebraic
• II-A3- Represent
methods.
functions in algebraic,
• II-C2- Use symbols to
graphical, and
represent unknowns
spreadsheet technologies.
and variables.
Alternative: Water Rockets
• Water rockets on
require water and air
pressure to make them
fly. This provides a
low cost solution to
the consumable solid
rocket models
Build or Purchase Water Rockets
$19.95
$129.95
www.pitsco.com
Phone: 1-800-835-0686
Home-made: $25.00
References & More Info
• Passing the South Carolina Exit Exam, by Frank Pintozzi
& Colleen Pintozzi, American Books, 1996.
• ALGEBRA II and Integrated Approach, by Roland
Larson, Timothy Kanold and Lee Stiff. Published by D.C.
Heath and Company, 1997.
• Estes Model Rockets (www.estesrockets.com):
Manufacture of model rocket kits, engines and accessories.
• NAR (www.nar.org): National Association of Rocketry.
• Model Rocketry for Educators
(home.earthlink.net/~voraze/toc.html): for teachers.
• PITSCO: Learning resources at www.pitsco.com