Dalek Pretorius

Math 1010; Project 3: Height of a Zero Gravity Parabolic Flight

Height of a Zero-G Flight t Seconds After Starting a

Parabolic Flight PathTime t in seconds 2 20 40Height h in feet 23645 32015 33715

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

Part 1; Write your 3 by 3 system of equations for a, b, and c:R1) 4a + 2b + c = 23,645R2) 400a + 20b + c = 32,015R3) 1600a + 40b + c = 33,715

Part 2; Solve this system. Do all computations on a separate sheet of paper (Attach supporting documents):a= -10

b= 685

c= 22,315

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

f(x) = -10x² + 685x + 22,315 or f(x) = -10(x – 34.25)² + 34,045.625

Part 4: Find the maximum value of the quadratic function. Do all computations on a separate sheet of paper (Attach supporting documents).

Max = 34,045.625

Part 5: Use the graphing program you’ve installed to graph the parabola obtained in Part 3. Copy and paste it into this document. Be sure to set the axes to the proper scale so that you see the vertex and x and y intercepts.

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 way you think, write how this project gave further evidence to support your existing opinion about applying math. Be specific.

Though the application of quadratics in a real situation is interesting to consider, it is not at all surprising that they are applicable. Math in itself is a language which transcribes the mechanics of reality in a manner intelligible to the human mind. This project acts as just one of many examples as to how math inconspicuously fits into our world. More specifically, the project exemplifies how one can determine a moving objects trajectory, maximum height, and even the distances and times in which it will reach this height. Such formulas are not only applicable in unorthodox situations like zero gravity flights, but also in situations as simple as tossing a ball.

f(x)=-10*x^2 + 685*x + 22315

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