Height of a Zero Gravity Parabolic Flight

Cayla Rushton Mr. Ekenstam

Math 101011/12/13

Introduction NASA and the Russian Space Agency use a special

plane to train their astronauts. This plane goes almost straight up then nosedives almost straight down again this freefall simulates 10-20 seconds of weightlessness as felt in the Space Station. This almost vertical fight is actually a parabolic flight path. What is this parabolic flight path? How high does this Vomit Comet go?

Data

Height of a Zero-G flight t seconds after start of flight path

2 sec 20 sec 40 sec

23645 ft 32015 ft 33715 ft

The data points were given as time is seconds and height in feet. An equation was also given, h= at^2 + bt + c. When we plug in the data points given we have three equations with three variables. This is a system of equations so all three variables, a, b, and c can be found. Once a, b, and c are known you plug those numbers in on the equation h= at^2 + bt + c.

Equation Solving this system of equations it

comes to be a=-10, b=685, and c=22315 the new equation is h=-10t^2+685t+22315. Now the max height can easily be figured.

When Maximum Height Occurs When t=-b/2a this is when the

maximum=h. So plug in b and a, then plug in t to the equation h=-10t^2+685t+22315 this is the maximum value or height. When the time is 34.25 seconds the plane is 34045.625 feet up in the air and this is as high as it gets in its parabolic flight.

Graph With the equation h=-

10t^2+685t+22315 this flight path can be graphed.

34045.5

34044.5

34543.533 34 35

Conclution This project has changed the way I think about how math

can be applied because this is real, and really needs to be figured. NASA is a real organization and these are real jets. There are pilots right now that need to know this information and I figured it. I wouldn’t go so far as to say I could fly it but I know exactly where they would be and the precise position they would be in. Most story problems are simplified and unrealistic so seeing one that is realistic makes the math more real and seem more useful in life in general as well.