Math

I am in Algebra II and my teacher is Erin Zarko.  My math class is very tiny, we only have 8 people in it which leads to a lot of one on one time which makes learning math a lot easier some times.

The project that we did this year in math for exhibition, was build a catapult.  I worked with James Shahan.  Here is my catapult right up....

The purpose of this project is to explore a concept that we have already covered in Algebra 2 this year and go deeper into the idea and equations.  Quadratics and parabolas were difficult for both of us and we felt like we would benefit from learning more and revisiting it. A quadratic is any equation in the second degree(axsquared+bx+c=0)  and a parabola is the way of graphing an arc.

Through using a catapult, we are attempting to explore the applications of quadratics in real life. As you may know, when objects are launched they fly in an arc, and this arc can be measured using quadratics.  The highest point is called the vertex. 

The first material that we got was bungee cord and all we could really think of making was a catapult/slingshot.  The ideas flew through the air and plans were drawn in the multiples.  Finally we put the ideas to work.  Our catapult has a base of 1 foot by 1,4”.  The bungee cords are held up by large medal screws.  The launching sight is about 2 feet long and is attached at the end of the base by a hinge.  In the actual equation the distance of the shot serves as the A value, and the height as the B value.

To measure this instrument you need to pull it back to the same place every time that you launch it so a smart decision would be to place it up against a wall and mark a place on the wall where you can make sure it goes that far back each time.  You can fire it multiple times and get the average distance it flies.  Then you take half of that distance and measure away from a wall.  That’s where you place the catapult and fire again.  Wherever the object that you are firing lands is the vertex of the parabola.  The Vertex is where the two ending points meet.  The point where the vertex is also the line of symmetry. A place on the graph where there is an equal amount of space on each side. A very simple way to describe the vertex is the middle, it is at the middle of the graph in the lowest or highest point.

In the real world this can be used to measure the trajectory of things like rocket ships.  The vertex would be the point where it comes back down.  When measuring this you need to know exactly how far this would go and by measuring different points on the line you can figure that out. 

 Sara Martin- Personally I was not very excited about making a catapult.  I’m not the most creative or artistic person and when we were thinking about ways to make it I could not think of any ways to make it work well.  We also thought that our catapult would be a lot bigger but it was easier and just as efficient to make a smaller one that shoots around twenty feet.  We thought that we would shoot water balloons out of it but the water flow would make it a lot harder to measure and get accurate results.  This project has given me a general understanding of the equations used to find parabolas.  While measuring the parabola you need to know the two starting points first.  And then you can find the vertex.  With knowing the vertex you can find other points on the graph.  This is the middle point and whatever the X value is, is also the line of symmetry so you know everything will meet up there. 

 James Shahan- I connected to this project mostly because it was exciting to actually do a project in math, we are a project based learning school and we have had very little exposure to doing projects. This is also good for me because it makes quadratics interesting, when we are talking about how to calculate the equation of the ark of flight I actually become excited! After we had built our catapult, we measured the distance that it shot five times, we then took the catapult half of its shooting distance away from a wall, dipped the ball in water, and measured how high it went. This was how we found our vertex, once back in the classroom we plugged in our averages and then converted the equation to standard form. The final step was to put the equation on paper, now that all is done, I must say I am very happy with our project and the project in general!