Height of a Zero Gravity Parabolic Flight

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Height of a Zero Gravity Parabolic Flight

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Height of a Zero Gravity Parabolic Flight By: Sydney Oplinger Period 2 Math 1010 Project

Have you ever wondered what it was like to fly in space? This lab you are about to take a look at will determine the maximum altitude the plane reaches on its parabolic path. You will take a look at the data, equations, and the quadratic model used to create a graph of the planes flight.

The Data Time (t) in seconds Height (h) in feet The data up above shows the height of a Zero-G flight (t) Seconds after starting a parabolic flight path.

Setting up the Equation To set up the equation you need to plug all the numbers into the following equation: Y=a*x^2+b*x +c Above is the 3 by 3 system of equations for a, b, and c. This is what it looks like after you square the variables

Solving the System SOLVE USING ELIMINATION To solve this system you need to use elimination so that you can find the values for a, b, and c I started solving using the first two equations cancelling A then I went on to cancel B and lastly solved for C After solving I was left with three answers Values A= -10 B= 685 C= 22,315

Forming the Quadratic Model To form the Quadratic Model you must plug in your solutions for a, b, and c into the following equation: h=at^2 +bt+c

Complete the Square The next step to solve the lab question is to find the maximum value of the quadratic function. To do this we must complete the square To Complete the Square: Step 1: Divide everything by “a”, in this case it is -10 Step 2: carry “c” over to the other side and change the sign Step 3: Divide “b” by 2 and square. Then add to both sides Step 4: Factor and bring “c “ back over and change it’s sign The answer is: H=(t+34.25)^2 -3404.5625

Graphing the Porabola Now it is time to graph the original data given to us and the maximum point we just found. The maximum point is T= 34.25 seconds H=34,045 Feet Maximum Point

Reflection No, I have always known that math can relate to the real world. Math is used everyday! Without math, man would of have never walked on the moon and cupcakes would never be made perfectly. Although this lab proved one more way math can be related to real life this project didn’t change how I view math and the various applications it has to the real world.