## Rocket project

write up:

**Cover letter:**

The finalized goal of this project was to build a highly functionable high flying water powered bottle rocket. In this unit we learned about the contributing factors to a rocket's flight. We focused on the role that physics plays on the rocket, as well as the mathematical contributions. In physics we focused on Newton's three laws and how they apply to rockets. In math we focused on quadratics and linear functions. We followed an engineering design process that focused on seven steps: Ask, Research, Imagine, Plan, Create, Test, Improve. The first step is used to get help with issues we are facing. For instance I asked for help with the size of my fins without throwing off the weight. Then we have Research. This step is used to get information on the specific measurements we follow to accomplish the task at hand. For example I did lots of research on the scale measurements in order to make a functional backslider. Next step is to imagine, this step is used to apply the research to your project. In this situation, I would use the research and imagine how I would apply it by figuring out the measurement scales due to the size of my bottle. Then we have created, this step is when you put the research into action. For example assembling the rocket. Finally we have, test and revise. These two steps work together and are used to improve your rocket. First while testing the rocket you see what goes wrong or how it could improve. Then you revise based on how your rocket did, and restart the process.

to describe a Rocket's flight because they help us understand the relationship between position, velocity, and acceleration over time. Quadratics are a mathematical equation to determine the measures of a parabola. A parabola is a U shaped curve that is used to describe the measures of an arc motion. The formula for quadratic equations are particularly useful when dealing with objects in free fall or in projectile motion, like rockets. The motion of a rocket can be broken down into different phases, such as the ascent, peak / apogee, and descent. During these phases the position, velocity, and acceleration of the rocket change. Quadratic equations allow us to model and analyze these changes mathematically. By using quadratics we can determine the Rockets maximum height, the time it takes to reach that height and other important characteristics. The formula for a Quadratic, Is ax^2+bx+c+0, this is what creates the parabola shape. We also learned about linear motion. Linear motion refers to the movement of an object in a straight line, without any change in direction. Linear motion is a fundamental mathematical concept to describe physics and is often described using equations that involve variables like distance, time velocity, and acceleration. This is useful to describe velocity because they show how the position of an object changes over time in a straight line. By using a linear function, we can relate the change in position of an object to the change in time. The slope of the linear function represents the object's velocity. A positive slope indicates the object is moving in a positive direction, while negative slope indicates it is moving in the opposite direction. Linear functions are also helpful describing acceleration. Acceleration measures how quickly an object's velocity changes over time. When using linear functions to describe acceleration, we can look at the rate of change of velocity. If the velocity is changing at a constant rate, the linear function that represents this change will have a constant slope. The slope of the line represents the acceleration of the object. G’s stand for gravity, and are the measurement of acceleration due to gravity. Which is 9.8 meters per second squared. This means that an object's acceleration increases by 9.8 meters per second, every second. Linear motion shows how objects move under g’s influence. A frame of reference is a way to describe the position, motion and interactions of objects. It provides a set of coordinators or reference points that we can use to measure and analyze the movement of objects. Linear functions can be used to define the relationship between different frames of reference. For example if you have four frames of reference you can use linear functions to describe how the position or velocity of an object changes when observed from each frame. We used this by counting the frames in a video of our rocket launching, we had a reference post, and counted the frames it took to pass that post. When a bottle rocket is in free fall, it experiences linear motion as it moves in a straight line under the influence of gravity. Linear functions can help to understand and analyze the rocket's motion during this free falling period. For example it helps us to describe the relationship between time and the rocket's position or velocity as it falls. This allows us to predict how high the rocket will go, how fast it will fall, and other important aspects of its motion.

In physics we spent lots of time researching Newton's laws and the sub categories of laws of physics that go into them. In this rocket project, we learned about projectile motion, and how velocity and acceleration are used in terms of a rocket. For instance Newton's first law being “an object at rest remains at rest unless acted upon by an external force, as an object in motion remains in motion until acted upon by an external force.” also covers inertia, net force equilibrium and normal force. Inertia is simply the object's resistance to changes in motion, which basically means unless acted upon the object stays in its original state of motion. Net force is the combination of all the forces acting upon an object at once. The total of all the contributing forces is the net force. So for example net force zero is when all the forces are balanced meaning the object is either at rest or remaining at a constant velocity. Normal force is a contributing force that helps objects stay at rest. It is the force that counteracts gravity due to Newton's third law stating that every force has an equal and opposite force. Normal force is exerted by a surface to support the weight of the object resting on it. This is what stops things from sinking through the ground. Newton's second law is that Force equals mass times acceleration. There are many factors that contribute to the calculation of this. For example to find the force which is measured in newtons, (fun fact newtons were named after Isaac newton!) you also have to take into account the friction and drag acting on it. There are two types of friction, static friction and kinetic friction. Static friction is the force that keeps objects in their state of rest. Static friction has a breaking point that is when just enough force is applied to the object to get it into motion. Then once the object is in motion the amount of friction on that object actually lowers. This is called kinetic friction. Kinetic friction is the resistance on the object when it is in motion. Drag is another thing that must be considered in this situation. Drag is the force that opposes the motion of said object. For example when a rocket is in flight, there is drag acting upon it slowing the rocket down, which is why parachutes slow the rocket down in descent. Due to the parachute's increase in surface area that causes an increase in drag. Another important factor is to use mass rather than weight. It is a common misconception that mass and weight are the same thing, however they are very different. Mass is the measure of matter in an object, while weight is the measure of force exerted on an object due to gravity. Newton's third law states that “every action has an equal and opposite reaction.” An example of this is when any two bodies interact. For instance if you were to lean on a wall the wall pushes back against you with an equal and opposite force. Because the two forces are equal in magnitude but opposite in direction, this is what stops you from falling through the wall. The two forces working together to balance out is called a system. In terms of rocket, the first law tells us that when the pressure is released, being the external force acting upon it. It is taken out of rest and put into a state of motion. Once in motion the external force causing it to fall out of motion is the drag and air resistance acting upon it. His second law tells us the force of the rocket based off of the rocket's mass and acceleration while being affected by drag. Finally his third law tells us that when the water shoots out of the rocket it pushes the rocket upwards. This shows the action of the water falling out, and the reaction of the rocket being thrusted up.

**Calculations**:

The first thing we did was create a picture of a right triangle that could represent the height of our rocket

Then we used SOH CAH TOA to calculate the max height our rocket could get. SOH CAH TOA is a synonym for the pythagorean theorem which helps to determine the side lengths of right triangles. I used TOA which stands for tangent to find the max height of my rocket. I did this by laying out my equation as tan(52.2)=0/61. Then I got o by itself by multiplying both sides by 61. After this it was written as tan(52.2) 60= o. After plugging this into desmos I got 78.66. We then used the video of our rocket to count the frames it took to pass our reference post. This was to help us determine the starting acceleration of our rocket. It took our rocket 3 frames to pass the reference post, then we divided 3 by 30 because that was the number of frames per second this gave us 0.1, which we then divided by 1.7 because this was the height of the reference post. This gave me 0.05882, which is the time in seconds it took to pass the post. We then divided the meters it had (1.7) gone by the seconds it took (0.1) to get the meters per second it was going (17 mps). I then calculated the wet and dry weight of the rocket. Meaning the weight of the rocket with water for pre launch, and take off, and the weight without the rocket for rising flight, and controlled descent. I did this by weighing it and dividing by 1000, which gave me 0.92 for the dry weight, and 0.15 for weight weight. I then took these two weights and multiplied them by the calculated force of gravity(9.81) giving me9.025 for the full rocket, and 1.475 for empty. Since acceleration is due to NET force acting on an object, the forces acting against thrust in this situation are gravity and drag. I then calculate the thrust force by first finding the acceleration. I did this by using my initial velocity after take off(17) and dividing that by the time of launch(6/30). This gave me 85. I then multiplied 85 by the mass of the rocket with water (0.92) to find the net force(78.2). Finally to find the thrust force I added the force of gravity to the calculated net force→78.2 + 9.025=8.72. I added the net force and force of gravity together, because the net force counteracts the force of gravity, so in order to get an accurate thrust force you have to. Then I used the formula→h(t)=-1/2(g)(t^2)+vbase o(t)+y base o and plugged everything in. This gave me h(t)=-½(9.81)(t^2)+17(t)+0.3. I then identified the A, B, and C terms which I then plugged into the quadratic formula:b±√(b²-4ac))/(2a) and used this to find the zeros. Tis gave me t= -0.02 and t= 3.48. 3.48 is the zero that represented my theoretical flight time because it was positive. Then I began calculating the time of max height of our rocket by counting the frames in the entire video. This turned out to be 105. Then I divided 105 by 30 because that's how many frames per second there are. This gave me 3.5. After this I graphed my height function in desmos to find my theoretical time of max height based on the graph. I used h(t)=-4.905 t^2+17+0.3 to get the two coordinate numbers, giving me the time of 1.733. To check my work I did a comparison of the time I dot from the graph and the time I got from the video. They were different by 1.8 seconds. To calculate the time my rocket lauded I counted the frames in the video(12). I calculated the time of descent by subtracting the time of max height from the time of touch down, giving me 8.5. Finally I divided the distance traveled/max height (78.3) by the time taken(8.5) giving me, 9.25 m/s^2. After graphing my final quadratics I discovered that the rocket doesn't actually follow a parabolic trajectory, because once the rocket begins to descend, for me it means backslide. It is no longer in a parabolic shape because the speed decreases significantly. Which would look more like this

**Blue print:**

Original blue print

final blue print:

**Discussion and Analysis:**

A freebody diagram is a visual representation of the way the forces are acting on an object. We commonly simplify the object to a box with a dot representing the center of gravity. We then use arrows to represent the forces acting on t and its length and direction show the magnitude and direction of the force.

This free body diagram shows the two forces acting on the rocket during pre launch. The only two forces present are gravity, and normal force. Because the object is at rest both arrows are equal meaning the rocket has a net force of 0 in this stage.

The free body diagram representing this stage of rocket flight is shown with only two forces. This is because during take off the only two forces present are force thrust, and force gravity. Force gravity is pulling the rocket down, while force thrust, fueled from the pressurized water in the rocket, is propelling the rocket up. Because the force of thrust is stronger the rocket goes up rather than staying in its state of rest. This is represented with the two arrows, the one pointing up being larger meaning the rocket is being thrusted up.

The rocket in rising flight now is out of fuel that is thrusting it upwards, meaning there is no longer a force propelling it up. Now there is just the force of gravitational pull and drag imposed on the rocket. Because both forces are pulling the rocket down in the opposing direction of the rocket, it begins decelerating.

Finally, controlled descent is back to net zero. This is because the two forces acting on it are equal. This means it is now falling at a constant rate. Directly before the method of controlled descent has begun is when the rocket hits terminal velocity.

**Reflection/ conference:**

I think that this project was a very innovative hands-on way of teaching math and physics cooperatively. This project forced me to grow in many different ways. For example in this project, I grew as a scientist by learning about the logistics of our everyday actions. For instance we went into depth on inertia, gravitational pull, speed/acceleration etc. This has allowed me to develop a deeper understanding of the way that things function and why. I also grew as a mathematician by seeing an application of the mathematical equations we are learning in school into real life. I also grew to be able to use math outside of the classroom in a logistical sense that helps to understand how things work and are applied. Something that helped me to grow in this situation was simply the resilience we had to have just to finish our rocket. This helped me as an engineer to use perseverance and determination to fuel my project. A specific example of content that helped me to grow was the blueprint. It combined my research, calculations, and knowledge overall about the subjects in order to make a plan for our rocket. Though you can only see simple changes in our two blueprints we made many design changes in between the two blue prints. It is one specific example of how far we have come and the things we have changed in order to get our final rocket. I think that this will help me in the future by being able to apply my knowledge directly to hands-on projects. This will also allow me to be able to use resilience and grit to push myself and be self reliant, while also being aware of the opportunities for growth around me.

## energy unit

This unit was incredibly significant to my growth as a learner. I think I grew as a learner in many different ways throughout this unit. For example, I think I grew as a person. I think this, because I was often put in a stressful situation and forced to use my persistence to get me through it. This helped me to use my patients and focus in situations that can be problematic. This is good practice, as in bad situations it is always better to stay calm. I think I also grew as an academic. I think this because I learned that we are often trapped in our own views and can be blinded from other societal issues/injustices.
I grew as a learner in this unit in many ways, through knowledge, and persistence, but also as a person and a collaborator. I think that this project has taught me so much, I specifically learned a lot in humanities. I think in humanities we began addressing the fact that society has people trapped in a bubble of simply their own existence, and only focus on issues that will impact them. This made me realize how blind the world is to its own impacts. Simply learning about environmental justice has allowed me to grow as a person, it showed me that I have a very small fraction of knowledge of our world and the complexities within it. It keeps me wondering what else may be going on that I have no idea about simply because I am privileged. I think that this unit has given me a larger perspective and sense of wonder. One challenge I have encountered in this project is simply being in a group, group projects are difficult for me. I have found that in group projects I typically end up having to do a good majority of the workload. Though this is not always the case It is a struggle especially when it is a big project with a small amount of time. One member and I have been working very well together, however I found a bit of a struggle with my other group members' communication and cooperation in this project. Though we are all putting in a lot of effort it has just been difficult often finding ways that people can help out and put in their best effort. Another difficulty we have found was simply finding ways to print our posters and make our project interactive. We overcame all these issues, by staying calm, being patient and resilient and adjusting to the issues that arose. For instance I found jobs that could be more fitting for our specific skills, and used all of our talents to the best of our abilities. This has helped me to grow as a learner, because it puts me in situations where I am forced to challenge myself and face difficult situations that may commonly arise. If I were to redo this project, I would try and find a way we could make our project slightly more interactive, just so it is more memorable for the audience and the information we are presenting will stick with them. It is already decently interactive, however this way it would be more beneficial to the audience. Along with this I would try and pick a new example for the essay we wrote. I think this would be beneficial because then I would be able to have learned more about the impact on people. Along with this this would have allowed me to learn more in depth about nuclear reactors fail mechanisms. Besides this I am incredibly happy with the way that this unit turned out. I think my group's final project was a beautiful, captivating illustration of the consumption methods of lights and how humans take energy for advantage. This unit has tremendously helped me to grow. It has been helpful for me to see the narrowed view we are taught. It has helped to open my eyes to the fact that we are trapped in a systematic societal cycle. Because of the way that we are socialized and the human factors that have input on all human opinions we are stuck in this type of cycle. I don't know if it is possible to escape this system, however simply being aware of it has brought such a widening to my view point. I think that this unit has allowed me to intensify a sense of curiosity I have. I think that this is the most important quality to being a learner, it allows you a motive and a sense of accomplishment moving forwards, growing and continuing to expand knowledge and viewpoints. |