For this quarter of our Math 10 class, we designed, built, and tested bottle rockets. We used many different aspects of math and science for this project, including SOH CAH TOA, Quadratics, Factoring, and completing the square. We used all of these in different ways to help us create and calculate the numbers for our rockets. Factoring helped us break down equations to solve them quickly, SOH CAH TOA helped us with our rocket calculations, Quadratics helped us simplify and graph functions and solve calculations, and completing the square helped us simplify and solve equations quickly.
We used the design process to help us create the best possible rocket given our constraints. We all thought of ideas that might make our rocket go very high, made some changes, and implemented them into our blueprint. Then, we designed our rocket and built it as a group. We tested our rocket and figured out some of our weaknesses. We fixed most of our weaknesses, but time constraints limited us to what we could change to make our rocket better. |
Time of Max Height
Our rocket launch was recorded to find the time of max height. Recording at 30 frames per second (FPS) we can count the frames that we see the rocket reach max height to figure out the time of max height. Our max height was roughly 41 Frames into the recording. If we take our recording fps (30), and our frames into the video (41), we can divide the 2 numbers by each other to find our time in seconds, 41/30=1.37. We now have our answer. 1.37 Seconds = Time of Max Height Max Height When launching our rockets, we recorded the angle at max height using an inclinometer and were tracking the angle from approximately 200 feet from the launch site. Using SOH CAH TOA, we can calculate the max height in feet. Using SOH CAH TOA, and imagining our vector as a triangle with a hypotenuse, opposite, and adjacent side, we can calculate the max height. We have an angle recorded of 50 degrees, acting as our angle of the triangle, and a distance of 200 ft, acting as our adjacent side. Using Tangent (TOA) which is opposite/adjacent, we can finish our calculations. 200tan(50)=x=238.351. The Inclinometer was 4.75 feet off the ground, so adding that we get, 238.351+4.75=243.101. Leaving us with our final answer. 243.101 Feet = Max Height Initial Velocity To find Initial Velocity, we took the equation, h(t)=-1/2(g)(t^2)+Vo(t)+Yo. Height given time equals negative ½ gravity times time squared plus initial velocity times time plus starting height. If we plug this in we get 243.101(1.37)=-(16)(1.37)^2+x(1.37)+1.5 . After solving it gives us the answer. 263.926 feet per second Theoretical Flight Time To find our theoretical flight time, we take our gravity, max-height, and starting distance and plug them into the equation, h(t)=-16^2+263.926+1.5. We then take our values and plug in the first, second, and third values, and plug them into the Quadratic Formula as A, B, and C. The Quadratic Formula gives us our two 0s. -0.00568, and 16.50105. We take our positive value, and that gives us our answer. 16.505105 Seconds = Theoretical Flight Time Launch Video |
ReflectionDuring this project our rocket building went great, the only problem was the landing of the rocket. The first time we launched our rocket we couldn’t do 100% power because of a leak. We launched the rocket at 40 psi and it didn’t go high at all. It nose dived but didn’t do much damage. We found the leak was in the tornado connector connecting the 2 bottles, we added teflon tape and the connector wasn't tight enough. We fixed the leak and launched it again the next day. There was still a leak but it wasn't as bad so we were able to launch at 80 psi. It launched 229 feet and nose dived, the backslider and the cone holding the backslider crushed. We had to get a new backslider and made a better parachute holder. We also replaced the tornado connector and we didn’t have enough time to do another test launch before the exhibition.
At the exhibition we did a successful launch and the parachute deployed at the last second. Even though our test launches weren’t fully successful our group learned a lot from the launches. Our successes were our test launches because of the tuning and refinement we could do to make sure it worked. For the next year sophomores I would tell them to keep doing as many test launches as possible and to keep refining their rocket to make it as good as possible. The biggest turning point in our project is after our second launch. We realized that the fins were making our rocket nose dive so we also made our fins a lot smaller to counter the nose dive. Another thing we realized was that our cone that was holding the parachute down was too tight and couldn’t come loose. We completely remade the top part of our rocket and made a better system to hold the parachute. Launching our rocket those 2 times were really important for the development of our rocket and helped us get 2nd place. In this project I didn’t just learn how to build a rocket, I learned what I was able to do as a team. While working together I felt I was able to assign everyone to a task to get the most work done possible. We split up to work on fins, backslider, parachute and when someone in our group finished that thing I was able to find something for them to do to help us. I felt in our project we were very efficient and I was able to be a leader and make sure everyone was busy helping. I love working with other people and I think I can be a leader to organize and guide people to be efficient in group projects. If I was going to do this project again I would make my rocket as simple as possible to make sure we can do as many test launches as possible. We spent a lot of time refining our rocket after a launch and we could have used that time to launch. Another problem in our rocket was our parachute so I would try to find a parachute system online that would work 100% of the time. In our class the rocket that went the highest was a single bottle rocket that went 359 feet which is crazy. I think that bigger the rocket isn't always better and it’s best to be simple. |
What is this project? |
Write Up |
In this project we learned about statistics. We learned about samples, chi-squared, and different examples of statistics. Our goal at the end of this project was to get real data from our school.
What did I do?For this project I wanted to see if there was a GPA difference between men and women at our school. First I did some research to compare my data to others. In the research I did I found that there was no difference in GPA between men and women. At our school we had a sample of 121 students and there was no difference in GPA between male and females.
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