Introduction: Zero Gravity

The assignment for this project shows the effects of zero gravity on astronauts during a NASA training flight in a test aircraft affectionately referred to as the vomit comet. Using a quadratic function the path of the aircraft is projected on a graph as a parabola, which makes an easy to understand visual representation of the aircraft trajectory.

This is found by using the three sets of given coordinates to write a system of equations, which I chose to solve using the elimination method, instead of the recommended augmented matrix.

Once the values of a, b, and c were found the quadratic function was written. I used the Vertex formula to find the vertex. I set t=0 and solved giving me the Y intercept. Using the vertex and Y intercept I plotted the graph.

Introduction: Advertising Campaign

The second assignment is a linear programming model used to maximize a company's advertising budget. Given the information provided I came up with five linear inequalities, written as a list of constraints, and an objective function. Solving the five inequalities I was able to plot them on a common XY plane. Using test points for each I was able to find the feasible region. One of the vertices was found to have a decimal value after solving by using the appropriate system of equations. The decimal value was rounded down as it’s not practical to have a partial ad.

Reflection:

When I was young I remember seeing the images on TV of the space shuttle going off to the unknown. Good pictures and bad, and how the world cried when it broke up, twice. I was about 10 years old and a big fan of Star Wars and this was just amazing to watch. When I first saw this project it prompted me to look up videos on YouTube detailing the fascinating engineless glide path that the Shuttle takes on re-entry. I didn’t know it was done with no engine power! What amazing math it must take to calculate that one and only chance at landing from ½ way around the world.

Although parabolic flight is something that most of us will never experience, this project is relatable to the real world, especially with the visual image projected on the graph. One can clearly understand the term “vomit comet”, while trying to imagine a plane taking the trajectory of the line on the graph. This math is the basis of the science that makes space travel possible. It reminds me of the movie Hidden Figures. Our civilization benefits in many ways because of space travel. Just as a business owner is interested in making a profit, NASA is interested in not killing its astronauts or destroying projects worth billions of dollars.

The optimization of advertisements project has made me think of other ways this could be used such as with farming. But specifically I’ve been thinking on what the limitations on constraints could be? For a seeding project it seems to me that a farmer could have an inequality for time of year, temperature, moisture, crop yield, etc. Or, couldn’t the guy buying advertisements also have constraints on what time of day or week the advertisements occurred? The results of the advertising campaign were surprising to me. If I was a manager working on this analysis for my boss I’d try to make him change his mind on twice as many TV as radio ads. Although it is intuitive that TV ads would be more beneficial the lab shows the opposite to be true. He would’ve reached more people with all radio ads. On the space flight, the lab shows the data which can be used to maximize training effect with zero gravity while also not killing someone. The political dynamic of science must be one of the most difficult areas for a mathematician or scientist to navigate while trying to convince a higher power that may have bias. I would expect the most powerful tool available would be the ability to be clear about the process justifying the conclusion.

This assignment didn’t change my thoughts on math one way or the other. I previously understood that Math is important, but how it was important was abstract. If anything, the solving of these two projects, has opened up many other questions that I’m excited to get on with finding out. My other class is Intro to AutoCad and I’ve enjoyed thinking about how the shapes make more sense than they would’ve without this class. I very much look forward to Math 1050 next semester.