Rocket Project
Project Description : For the final project in math 10 this year we were tasked with creating a bottle rocket that could be launched at 100PSI.
Cover Letter and Calculation's
Cover Letter
This year in math 10 we worked on various topics. And for our final project we learn how to apply them in real-world situation through the rocket project in which our objective was to create a rocket for plastic bottles, trash bags string, super glue and whatever else we could fin around the classroom so that we could have a rocket that coud be successfully launch at 100 PSI. now to do this we learned how to use quadratic functions and how quadratic function relates to projectile motion.( A projectile is an object that rises and falls under the influence of gravity and the quadratic function help us understand of it work and what path it takes),. and SOH CAH TOA to calculator our variables which included position( the place in where our rocket is located) velocity(the speed of our rocket in a give direction) and acceleration (the increase in the rate or speed of which our rocket moves).
. This process was introduced to us at the beginning of the unit through a mini project where we created catapults. We started by creating a blueprint which was the beginning stage of the engineering design process (ask, research, and imagine) and eventually testing, followed by improvement from our trial and error (plain, create, test, and improve). Then we took this into a bigger scale and in more depth when creating our rockets. Learning this process was our guide on this project and allowed us to create an end result we felt good about and was put together with care.
Calculations
Time of Max Height
To find the time max height we first viewed a video that shows our rocket launching and its flight. We found that 12 frames on an iPhone is equal to the max height of our rocket. Because on an iPhone it moves 30 frames per second, we count how many frames it takes for our rocket to reach max height, this allows us to divide our frames by 30. In this case we had 12 frames so we would divide 12 by 30. So this means that our time of max height would be .4 seconds.
Max Height
When calculating max height our first step was to find the angle of the rocket. In our case the angle was 19. We calculated using SOH CAH TOA and applied the angles we know to the equation. Using SOH CAH TOA we took y/200 times 200 followed by taking our found an angle of 19 and plugin that into tangent which SOH CAH TOA shows us to use. So the equation would be y=200tan(19) and if we plug that into a calculator y= 68.86ft, so this means the max height is 73.61.
Initial velocity
The next step was to find the initial velocity of our rocket, which is the velocity at which the motion starts.
To find the initial velocity, we use the max height and time of max height to solve for the initial velocity which looks like this ]
h(t)=-12(g)(t)^2+Vo(t)+yo
68.86=-12(32)(0.4)^2+Vo(0.4)+1.5
68.86=-16(0.4)^2+Vo(0.4)+1.5
68.86=-2.56+Vo(0.4)+1.5
68.86=-1.06+Vo(0.4)
+1.06 +1.06
96.92/0.4=Vo(0.4)/0.4
Vo=175.8ft/s
and this is our initial velocity
Theoretical flight time
our final step was finding the theoretical flight time and to do that we used the Stander Form of a Quadratic ax2+ bx+c and the Quadratic Formula
-bb2-4ac
X = 2a
Aswell as the formula for height at any given time: h(t)= yo+Vo(t)-12(g)(t2),
h(t)=-12(32)t2+175.8xt+1.5
a=-12(32)=-16
b=175.8
c=1.5
-175.8175.82-4(-16)(1.5)
X =
2(-16)
t=-0.01
t=11.0 total flight tome =11sec
Time of Max Height
To find the time max height we first viewed a video that shows our rocket launching and its flight. We found that 12 frames on an iPhone is equal to the max height of our rocket. Because on an iPhone it moves 30 frames per second, we count how many frames it takes for our rocket to reach max height, this allows us to divide our frames by 30. In this case we had 12 frames so we would divide 12 by 30. So this means that our time of max height would be .4 seconds.
Max Height
When calculating max height our first step was to find the angle of the rocket. In our case the angle was 19. We calculated using SOH CAH TOA and applied the angles we know to the equation. Using SOH CAH TOA we took y/200 times 200 followed by taking our found an angle of 19 and plugin that into tangent which SOH CAH TOA shows us to use. So the equation would be y=200tan(19) and if we plug that into a calculator y= 68.86ft, so this means the max height is 73.61.
Initial velocity
The next step was to find the initial velocity of our rocket, which is the velocity at which the motion starts.
To find the initial velocity, we use the max height and time of max height to solve for the initial velocity which looks like this ]
h(t)=-12(g)(t)^2+Vo(t)+yo
68.86=-12(32)(0.4)^2+Vo(0.4)+1.5
68.86=-16(0.4)^2+Vo(0.4)+1.5
68.86=-2.56+Vo(0.4)+1.5
68.86=-1.06+Vo(0.4)
+1.06 +1.06
96.92/0.4=Vo(0.4)/0.4
Vo=175.8ft/s
and this is our initial velocity
Theoretical flight time
our final step was finding the theoretical flight time and to do that we used the Stander Form of a Quadratic ax2+ bx+c and the Quadratic Formula
-bb2-4ac
X = 2a
Aswell as the formula for height at any given time: h(t)= yo+Vo(t)-12(g)(t2),
h(t)=-12(32)t2+175.8xt+1.5
a=-12(32)=-16
b=175.8
c=1.5
-175.8175.82-4(-16)(1.5)
X =
2(-16)
t=-0.01
t=11.0 total flight tome =11sec
Rocket Blue Print
Rocket launch Video
Reflection
Reflection
During this project, the biggest challenge I faced was my group pairing. Before this project started, I advocated not to be put in a group with a certain person because I had a history with struggling with doing group work with them before in which I always and I mean always ended up doing everything in the project wall they wondered around doing nothing to contribute. So when I found out who I was pared with I went to my teacher to try to advocate for myself and was immediately shut down after one word and try then seeing if my adviser could help me but she couldn't and I also talk to another teacher that was willing to Listen but. that still weren’t able to help, so to answer the question, I was not able to navigate my biggest challenge. I just had to tough it out.
my rocket flue and didn’t blow up that was the biggest success I had during this project and my advice for next years sophomores is that if you end up splicing don’t be afraid to really lather on that glue and when in doubt keep it easy and don’t over engineer. Also, don’t give up on advocating for yourself.
This project for me was just a straight up struggle. There was no turning point. There was just me doing over half the work in a three-person group and waiting for this project to end because honestly the rocket project was my least favorite project this year.
I learned that advocacy doesn’t always work and when it come down to it sometime the best thing you can do is tough it out because that's the only way to get to the other end, I also learned that I have some amazing friend that are there for me when I need them and are willing to listen and help me through the rough patches just like I am there for them.
If I did this project again, I would fight harder on being in a group where everyone does equal work. And the reason behind this is that over the past three years of covid-19 my mental health has gone up and down a lot so being shut down ignore and over worked. Doesn’t help me in fact it make me hate school it makes every time I step in class something I dread and it also make me hate myself because it make me feel like I am not worth listening to and that hurts.
During this project, the biggest challenge I faced was my group pairing. Before this project started, I advocated not to be put in a group with a certain person because I had a history with struggling with doing group work with them before in which I always and I mean always ended up doing everything in the project wall they wondered around doing nothing to contribute. So when I found out who I was pared with I went to my teacher to try to advocate for myself and was immediately shut down after one word and try then seeing if my adviser could help me but she couldn't and I also talk to another teacher that was willing to Listen but. that still weren’t able to help, so to answer the question, I was not able to navigate my biggest challenge. I just had to tough it out.
my rocket flue and didn’t blow up that was the biggest success I had during this project and my advice for next years sophomores is that if you end up splicing don’t be afraid to really lather on that glue and when in doubt keep it easy and don’t over engineer. Also, don’t give up on advocating for yourself.
This project for me was just a straight up struggle. There was no turning point. There was just me doing over half the work in a three-person group and waiting for this project to end because honestly the rocket project was my least favorite project this year.
I learned that advocacy doesn’t always work and when it come down to it sometime the best thing you can do is tough it out because that's the only way to get to the other end, I also learned that I have some amazing friend that are there for me when I need them and are willing to listen and help me through the rough patches just like I am there for them.
If I did this project again, I would fight harder on being in a group where everyone does equal work. And the reason behind this is that over the past three years of covid-19 my mental health has gone up and down a lot so being shut down ignore and over worked. Doesn’t help me in fact it make me hate school it makes every time I step in class something I dread and it also make me hate myself because it make me feel like I am not worth listening to and that hurts.
Cookies Project
Problem Statement
Sweet tooth baked goods sell fudge and toffee every Tuesday and Thursday. It cost 0.53 to make a piece of fudge and 2.12 to make a batch of fudge after the 300% markup and toffee cost 0.22 per piece of toffee and 0.88 per batch of toffee after 300% markup and their total budget is 500 dollars. It take them 95 minute to make a batch of fudge which is 16 piece and 80 minutes to make a batch of toffee which is 32 piece and have 780 minutes to make them. Fudge needs 3 cup of chocolate chip and toffee needs 2 cup of chocolate chip and they have a total of 25lb of chocolate chip. Now give this information how much of each item should Sweet Tooth Baked Goods make to have the best total profit.
Sweet tooth baked goods sell fudge and toffee every Tuesday and Thursday. It cost 0.53 to make a piece of fudge and 2.12 to make a batch of fudge after the 300% markup and toffee cost 0.22 per piece of toffee and 0.88 per batch of toffee after 300% markup and their total budget is 500 dollars. It take them 95 minute to make a batch of fudge which is 16 piece and 80 minutes to make a batch of toffee which is 32 piece and have 780 minutes to make them. Fudge needs 3 cup of chocolate chip and toffee needs 2 cup of chocolate chip and they have a total of 25lb of chocolate chip. Now give this information how much of each item should Sweet Tooth Baked Goods make to have the best total profit.
Solution
Project Reflection
What is something you are proud of from this unit, and if you were to do this project again how would you refine it further?
I am proud of myself for finishing this project on time because I was sick last week and was out of it which caused me to feel like I had been left in the dust and I didn’t really started to get my information down till Monday the following week and finish my graph that night as well and I know me being sick wasn’t the only thing working against me during this project because there were differently parts where I found myself stuck and struggling but sense I have always had this I can figure it out myself mentality I got set further back but I know this is something I struggle with and am working on it this year so if I were to do this project again the one thing I would change is to ask for help when I needed it.
What is something you are proud of from this unit, and if you were to do this project again how would you refine it further?
I am proud of myself for finishing this project on time because I was sick last week and was out of it which caused me to feel like I had been left in the dust and I didn’t really started to get my information down till Monday the following week and finish my graph that night as well and I know me being sick wasn’t the only thing working against me during this project because there were differently parts where I found myself stuck and struggling but sense I have always had this I can figure it out myself mentality I got set further back but I know this is something I struggle with and am working on it this year so if I were to do this project again the one thing I would change is to ask for help when I needed it.
Tessellation Project |
In math 10 this year are first big project was on make are own tessellations we study many different topic in this proses like how can we measure efficiency, what is the most efficient shape and how you can prove two triangles are similar and so much more all these topic have helped me better understand the importance of geometry because geometry is infected everywhere we see it in nature everyday with salt column beehives and the Fibonacci sequence because nature love efficiency and geometry it all about efficiency. These concept not only help me better understanding geometry better but also helped prepare me for make my tessellation but even with all this information I was till bound ran into problems like one does when trying something new and my biggest problem was making the perfect stencil to tessellata but it turns out cutting a perfect stencil it pretty much impossible which lead to plenty of failed prototypes and designs from uneven edge and I did eventually give up on the stencil and founded a repetitive pattern I could tessellate without a stencil which turn my tessellation into something completely different from my original idea but despite that I'm still happy with the finished product because it gave make the chance to work on my growth and adaptive mind set throughout the project.
Now at the start I listed different thing we had learned throughout this project above and apart of the project was to answer two of them I choice to answer ( how you can prove two triangles are similar to which the answer is If two pairs of triangles angles are corresponding angles of congruent, triangles make the triangles similar and if We know two of the angles are the same on your pairs of triangles then the third side of your triangles must be equal as well. Then we know are two same angle will make the third angle the same length which gives us three angle pairs that are all equal,
In proportion to each other proving them similar and the other was How do you find the area of a polygon with n sides? Now since the sum of all the interior angles of any triangle is 18 0 ∘ 180^\circ 180∘, the sum of all the interior angles of an n side polygon with n n n-sided polygon would be equal to the sum of all the interior angles of ( n − 2 ) (n -2) (n−2) triangles, now if we apply this we can fined the area of an n side polygon. I have learn that there is so much more to geometry then just shape and that understanding geometry can help you better understand the very world around you.
Now at the start I listed different thing we had learned throughout this project above and apart of the project was to answer two of them I choice to answer ( how you can prove two triangles are similar to which the answer is If two pairs of triangles angles are corresponding angles of congruent, triangles make the triangles similar and if We know two of the angles are the same on your pairs of triangles then the third side of your triangles must be equal as well. Then we know are two same angle will make the third angle the same length which gives us three angle pairs that are all equal,
In proportion to each other proving them similar and the other was How do you find the area of a polygon with n sides? Now since the sum of all the interior angles of any triangle is 18 0 ∘ 180^\circ 180∘, the sum of all the interior angles of an n side polygon with n n n-sided polygon would be equal to the sum of all the interior angles of ( n − 2 ) (n -2) (n−2) triangles, now if we apply this we can fined the area of an n side polygon. I have learn that there is so much more to geometry then just shape and that understanding geometry can help you better understand the very world around you.