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FlightMath 1010 Intermediate Algebra Group Project

Have you ever wondered what it might feel like tofloat weightless in space? One way to try it out is tofly on a special aircraft that astronauts use to train for

their trips to space. Both NASA and the Russian SpaceAgency have been flying these for years. The way thisis accomplished is to fly to a high altitude, drop downto gain speed, and then start a large parabolic path up

in the sky. For a time ranging from 10 to 20 seconds,

along the top part of the parabolic flight, an

environment simulating zero gravity is created within the plane. This effect can cause some nausea inthe participants, giving rise to the name "Vomit Comet", the plane used by NASA for zero-G parabolic

training flights. Currently there is a private company that will sell you a zero-G ride, though it is a bit

expensive.

This lab will have you take a look at the parabolic path to try to determine the maximum altitude theplane reaches. First, you will work with data given about the parabola to come up with a quadratic

model for the flight. Then you will work to find the maximum value of the model. Now for the data:

Height of a Zero-G Flight t Seconds AfterStartina a Parabolic Fliaht Path

Time t in secondsHeight h in feet 2364~ I

x

20 I "'"

337~~ I32015

To find the quadratic model, you will be plugging the- data into the model h = at2 + bt + c.The data points given are just like x and y values, where the x value is the time t in seconds andthe y value is the altitude h in feet. Plug these into the model and you will get equations with a,band c.

t of equations for a, b, and c.Part 1: Write your 3 by 3.S

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h (2O}::: "l (LO) L! \0 (16J fC = 4001:i t 2-0 \> \- C = '72010

h (~O 1 " C\ C 20 ) 2- t b ( 20 ) H = I ~ 0 0 q -f 10 b tc = ~ ~ 7 I~

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Part 2: Solve this system. Make sure to show your work.

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- 120 t- b :: Lj &'7

b'= 4foC? - LZ,\

\ ~ 0 0 tit i~ci c(/ q "S - 2 L u) t l & &'1t; -' LI tt - 2 h -~ ~ ~lit;

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I( G 0\ - 2- b -=- ~ CO t; 2; ()

-\ \ 0 0\ - 1 CL\ ~ S - LL q') =. - ~ 5 1:; C\

1 \\?J (;, 'r ~qq .~ .~q;~7)O t- ., I; ()

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Part 3: Using your solutions to the system from part 2 to form your quadratic model of the data.

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Part 4: Find the maximum value of the quadratic function. Make sure to show your work.

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~-Cf~o~g~~ i:EPart 5: Sketch the parabola. Label the given data plus the maximum 'poTiiT.p; gooa way to start labelingyour axes is to have the lower left point be (0, 20000)

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(-t )Part 6: Reflective Writing.

Did this project change the way you think about how math can be applied to the real world?Write one paragraph stating what ideas changed and why. If this project did not change theway you think, write how this project gave further evidence to support your existing op inionabout applying math. Be specific.

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