Height of a Zero Gravity Parabolic FlightMath 1010 Intermediate Algebra Group Project

Have you ever wondered what it might feel like to float weightless in space? One way totry it out is to fly on a special aircraft that astronauts use to train for their trips to space. BothNASA and the Russian Space Agency have been flying these for years. The way this isaccomplished is to fly to a high altitude, drop down to gain speed, and then start a large parabolicpath up in the sky. For a time ranging from 10 to 20 seconds, along the top part of the parabolicflight, an environment simulating zero gravity is created within the plane. This effect can causesome nausea in the participants, giving rise to the name "Vomit Comet", the plane used byNASA for zero-G parabolic training flights. Currently there is a private company that will sellyou a zero-G ride, though it is a bit expensive, around $5000.

This lab will have you take a look at the parabolic path to try to determine the maximumaltitude the plane reaches. First, you will work with data given about the parabola to come upwith a quadratic model for the flight. Then you will work to find the maximum value of themodel. Now for the data: H' ,\~.t c. r: \' \r-l. I Sera . J S

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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.

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Part 1: Write your 3 by 3 system of equations for a, b, and c."\d \ <::: (/') 'I.~..•••.SO 6) (\ J \ 'Z...SQ \~..\o, r,:,:",\ v-; "" .••• L \ -'- \)

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

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

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

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Part 5: Sketch the parabola. Label the given data plus the maximum point. A good way to startlabeling your axes is to have the lower left point be (0, 25000)

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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 the wayyou think, write how this project gave further evidence to support your existing opinion aboutapplying math. Be specific. \, J

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