Rocket project
cover letter
The Goal of the rocket project was to try to build a rocket that has the ability to launch the highest. Using air pressure and water to act as a force of thrust. Once our rocket was launched and reached its apex we also needed a mechanism to control the decent portion of our rockets' flight. After we had completed our launch, when we used math to graph our rocket launch using the quadratic formula, this formula showed us the height of the rocket at each portion of our launch. To try to build our most optimal rocket we went through many stages of the Engineering Design Process . These stages are to define the problem, conduct research, brainstorm and conceptualize, Create a Prototype, Select & Finalize, Product Analysis, Improve Product Design. These stages are used to find a solution to a problem by being able to test your theory and change wearables to find a result. This was very helpful in our rocket when we were test launching because we could change one aspect of our rocket like the fins and see how it affected our rocket during flight.
When describing the flight of a rocket we need to use a quadratic equation which is a function with an unknown term to the power of 2. Because of x being to a power of 2 in a quadratic equation it leads to an arch shaped graph. Position of a rocket overtime is shown by a single point on the graph.(Time since launch,Rocket height) We can also find the average velocity of our rocket at a certain height by dividing it by the time since launch. A parabola also shows the change in acceleration over time at a constant rate of 9.8 m/s the curve of the graph represents the acceleration to 0m/s at the apex of the rocket's flight. Our rocket is graphed at which we are just focused on liar motion on the y axis with the horizontal motion of the rocket not affecting the motion of our rocket.
Newton's first law of motion. Every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is used in our rocket project because the Inertia of our rocket wants to stay on the ground pre launch leaving to use an external force of thrust to change the motion. When the object is at rest on the ground the net force is zero because the object is at rest and the normal force and gravity are balanced. Newton's second law of motion is force= mass x acceleration. We can use this to find the amount of force applied to our rocket, During each stage of flight. Newtons 3rd law is that every action has a equal and opposite reaction. An example of this for our rocket launch when the rocket is launched the force of the water pushing into the ground helps create a force of the ground pushing back giving our rocket flight.
When describing the flight of a rocket we need to use a quadratic equation which is a function with an unknown term to the power of 2. Because of x being to a power of 2 in a quadratic equation it leads to an arch shaped graph. Position of a rocket overtime is shown by a single point on the graph.(Time since launch,Rocket height) We can also find the average velocity of our rocket at a certain height by dividing it by the time since launch. A parabola also shows the change in acceleration over time at a constant rate of 9.8 m/s the curve of the graph represents the acceleration to 0m/s at the apex of the rocket's flight. Our rocket is graphed at which we are just focused on liar motion on the y axis with the horizontal motion of the rocket not affecting the motion of our rocket.
Newton's first law of motion. Every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is used in our rocket project because the Inertia of our rocket wants to stay on the ground pre launch leaving to use an external force of thrust to change the motion. When the object is at rest on the ground the net force is zero because the object is at rest and the normal force and gravity are balanced. Newton's second law of motion is force= mass x acceleration. We can use this to find the amount of force applied to our rocket, During each stage of flight. Newtons 3rd law is that every action has a equal and opposite reaction. An example of this for our rocket launch when the rocket is launched the force of the water pushing into the ground helps create a force of the ground pushing back giving our rocket flight.
Blue Print
Calculations
To find the max height of our rocket we used Tan. This is because we already knew the adjacent value for our triangle and tan shows you what the opposite value is which in our case was the height of our rocket. So the equation I used was tan(55.31)=x/61 so once we have our equation we need to solve for x by multiplying both sides by 61 to get x by itself. Once you do this you get 88.12. Now you must account for the height of the rocket and the angle measurer. So we know that the rocket is .3m and the angle measures to the height and so we get a final rocket height of 89.32m. Sense we didn’t have a rocket video we needed to solve a equation to find the initial velocity. The equation that we used was the height over time formula. We were able to find our velocity by getting V by itself. Our starting velocity was 42.17m/s. The next thing we needed to calculate was the amount of gravity acting on the rocket by finding both the wet and dry weight of the rocket. The process of finding this is by finding the weight of the rocket and multiplying it by 9.81. For my dry mass I had 0.149kg and my wet mass our rocket was 1.014kg. To find the gravity the last thing we did was multiply it by 9.81 which is the acceleration due to gravity to use the f=m x a formula. Witch gave me a force of 1.46N for the dry mass and a force of 9.94N on the wet mass. To find the thrust force you need to first need to use dry mass of our rocket witch is 0.149kg times 250.5 because that is the velocity of the acceleration that our rocket experiences. Once we find this force at 37.32N we need to add the force of gravity to the value because the thrust is also overpowering this force pulling it down. So you add 1.46 to the original force for a total force of thrust of 38.78N. This graph of our rocket time shows the theoretical flight time as you can see the rocket reaches a max height at 4.22 seconds. The only problem with this is that it doesn't account for having a controlled descent mechanism. This is because there is a backsliding mechanism to slow down the rocket during its descent. So because we can’t use that as our descent we needed to solve for the decent time. The way we did this was by looking at someone with a similar rockets decent video and counting the frames. Once we had the decent speed of 6.78 m/s we divide the max hight of 89.3m by 6.78 to find a decent time of 13.17. Our last step is to find our total flight time together so we add 4.2 our time of max hight together with 13.17 to get a total flight time of 17.37 seconds.
Reflection
How did you grow as a Mathematician? I think this rocket project has really helped me grow to be more of a problem solver in math because throughout my life I have felt good at solving equations on a page but during this process I had to figure out how to apply those equations to real life situations. And that was difficult for me.