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.
Anysis
There are 4 stages of flight that our rocket experiences. The first being when the rocket is in the pre launch phase. During this phase there are only 2 forces acting on the rocket. These 2 forces are the force of gravity pulling the rocket to the ground as well as the normal force that's equal to the force of gravity in the opposite direction. Newton's first law of inertia is what is holding the rocket at its standstill because an object wants to stay at a point of rest.
The second stage of flight is the take off phase of launch. During this stage is when the water is pushing out of the rocket using Newton's 3rd law with the action of pushing the water into the ground lifts the rocket in the opposite direction into the sky. Newton's second law affects this stage of flight because acceleration=force/mass. This is used because when you have a smaller mass rocket it would need a lot less force to have the same amount of acceleration as a larger rocket. In this stage the free body diagram shows a stronger force of thrust because the rocket is accelerating.
The 3rd stage of launch flight is rising flight. This is after the rocket releases all of the thrust. During this stage Newton's first law of inertia is trying to keep the rocket flying through the sky. But the force of gravity is pulling the rocket down decelerating the rocket until it reaches a velocity of 0m/s at its apex. For this stage the free body diagram only has one force of gravity acting on the rocket; this is because there is no more thrust and it's just the rocket's inertia keeping the rocket flight up.
The fourth and final stage of rocket flight is controlled during this stage when the rocket reaches terminal velocity. When the rocket's drag is equivalent to the force of gravity balancing out to a constant speed and reaching a net force of zero since the drag and gravity cancel each other out. The forces on the free body diagram are balanced because the rocket is moving at a constant velocity.
The second stage of flight is the take off phase of launch. During this stage is when the water is pushing out of the rocket using Newton's 3rd law with the action of pushing the water into the ground lifts the rocket in the opposite direction into the sky. Newton's second law affects this stage of flight because acceleration=force/mass. This is used because when you have a smaller mass rocket it would need a lot less force to have the same amount of acceleration as a larger rocket. In this stage the free body diagram shows a stronger force of thrust because the rocket is accelerating.
The 3rd stage of launch flight is rising flight. This is after the rocket releases all of the thrust. During this stage Newton's first law of inertia is trying to keep the rocket flying through the sky. But the force of gravity is pulling the rocket down decelerating the rocket until it reaches a velocity of 0m/s at its apex. For this stage the free body diagram only has one force of gravity acting on the rocket; this is because there is no more thrust and it's just the rocket's inertia keeping the rocket flight up.
The fourth and final stage of rocket flight is controlled during this stage when the rocket reaches terminal velocity. When the rocket's drag is equivalent to the force of gravity balancing out to a constant speed and reaching a net force of zero since the drag and gravity cancel each other out. The forces on the free body diagram are balanced because the rocket is moving at a constant velocity.
Blue print
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.