Algebra 2 Write-Up
The thing that we looked into was Parabola’s and graphing equations. We first started out measuring the length of the shot and we marked where it landed. Then we got an extra point which we added to the graph which really helped us to get the full parabola. Then we used a calculator to get the equation. We also used it to get equation to go into a graph which then we can use to tell how far we would need to be if we were to change the length of where our target is. Our project changed pretty dramatically from one idea to another. We started out looking to find a catapult. We made a small idea into a 3d mini-model. After that, we realized that it wouldn’t be able to go as far as we thought or needed it to be. We got rid of the 3d model and began to construct a new idea. We felt like a ballista would be great to shoot the length that we wanted. As we started to create the ballista top, we thought that the base would be very difficult to make so we decided to make a crossbow and we would use something to keep it in the same place on either one of our hips. We tested who was a better shot and after we decided, we created something that would always be able to be stable in a somewhat 45 degree angle. We shot it a few times and felt that it was about the perfect degree that we could make it into the basket at the end of exhibition.
As we were building it, we got more intrigued into how we could make it better and shoot farther. Our idea right now was pretty difficult to create, but it was definitely worth it because it has enough power to shoot a good distance and we have control of it so that we can make it shoot where we would like it to. Once we actually got into it, it really felt like we were doing 3d graphing because we had to use the z-axis to get our parabola which we thought was very relaxing because it wasn’t really something that we weren’t bad at. Once we got to the parabola, we created it quite fast, but after we passed that and began to get our equation for our graph, this was where it got pretty hard. We asked for help and we slowly began to get through it which really helped us to make it the best that we could. Once we got this, we could always tell where we would need to stand and how many feet we would have to be back so that we could always make it a perfect shot. We used the original equation which is Y = a(x-q) (x-p). We had two points which they were (2, 3) and (0, 45). We held up a trashcan so that we could get one more point which, as you know, this can get out parabola. We got (35, 7) and after we plugged that in, we could use this to plug these into our graph. After we got our last point, we plugged it into our original equation which then we subtracted the q which lead to y=(x) (x-48). We plugged the x in which then was Y = (37) (37-48). After doing some quick subtraction and multiplication, we got 7 = (-0.017x) (x-48). We had to multiply -0.017x by x and -48. After we did this, we finally got the actual equation.
My math class this year is small but it allows us to get more work done. this year we have gone over stuff like 3-D graphing. Some of this stuff I get right away but the some I struggle with
