Leah Starr
Math Catapult Project
My catapult is exploring the aspects of a parabola. Parabolas are graphed by an equation that is to the second degree and three coefficients of constants. It always creates a curve which can be stretched or shrunk depending on your coefficient “a.” There are many ways to find the equation for a parabola. The way I am exploring is finding it through matrices.
The finished equation is: y=
The catapult is made of a rat trap for the spring and a wooden spoon for the arm. Then there is cut wood for the frame and base. When it is launched I will find the start point and the end point. These are the x-intercepts for the parabola. The start point is my first and my end point is my second. Neither of them will have a number in the y-spot. From there I will then launch at a wall to find another point, which will have numbers in both the “y” and “x” spot. I must also make sure that I use the same object each time to keep the speed and weight the same. That way my data will stay the same so create an equation. With two points I can put them into a metrics to find the equation of the parabola. This will be in standard form. From here I can figure the equation to hit a target. I can do this by seeing how far it is and how high it is above the ground. Then I can plug this into my equation to see where I need to place my starting point. The equation I will use is: y= .
I had originally planned on making a rat trap catapult but I soon found I wanted to do something different. I found a catapult online that you could make at home. It is called the ogre catapult and is two feet long. It is a lot bigger than a rat trap but it is less dangerous of breaking your fingers. Catapults help people figure out parabolas and what the drop rate is for certain weights and velocities; what distance you need if you are shooting a person out of a cannon onto a padded spot. If you know a starting point and an ending point from testing on a hug padded area you will be able to figure out how to aim the person onto a smaller square without killing them. Parabolas are also used in creating concave objects such as circles, tables, and even satellite dishes. Creating two that are mirrored to each other will make a circle object.
