Blue Print:
Cover Letter:
This semester in Math 10 we were learning about how to create a high-flying water rocket that has some sort of parachute before it lands. In math we learned about quadratic equations, representing velocity using vectors. Quadratic equations are equations where the largest exponent above a variable is 2. In physics we focused on Newton's 3 laws of motion. While making these rockets we used the engineering design process. The engineering design process is made up of 7 steps. First you ask a question or find a problem. We did this when starting the process and asking how we can build a rocket out of a bottle and create a parachute deployment system that works. Next you research. Which means finding the cause of the problem and the details. After you know details about the problem you can start to imagine how to solve the problem. When researching we looked at what other people did and how they built their rocket. Next you will be planning out an idea to solve your problem. We used this when drawing our blueprint and deciding what each aspect was going to look like. Next you need to create a prototype. This is when we started building our rocket. In this step you are using all of the research and knowledge from the other steps. Then you Test. In this step you are evaluating the prototyping to see what you can change and what works. After testing you will improve your prototype and fix the things that didn't work while testing, to create your final prototype. We did this by changing things about our rocket that didn't work the first time.
This September in math we learned about quadratic equations, representing velocity using vectors. Quadratic equations are equations where the largest exponent above a variable is 2. We can use these quadratic equations to help figuring out different aspects of our rocket including initial velocity, time, and height. We can define a quadratic function as y+x2. The position represented on the height vs time graph can be represented by a point where the rocket's height is given time. The velocity on the graph can be represented because the slope is the velocity. The acceleration is represented because acceleration is the curve itself and represents a change slope or changing velocity. A quadratic function can be represented as h(t) = , g represents the acceleration from gravity, and represents the initial velocity, and it represents the object's initial height. Velocity is the direction of the movement of an object. While acceleration is the rate of change of velocity. G represents gravity.
This semester in physics we focused on Newton's 3 laws of motion. Newton's first law is “An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.” This law includes inertia, net force and normal force. Inertia is the property of matter by which it continues in its existing state of motion unless it is changed by an external force. The net force results in a change in motion. The force that creates all of the pushing and pulling forces that are actually applied to an item is known as the net force. Which results in an object that will accelerate in the direction of the net force if the forces pushing and tugging on it are out of balance, or if there is a net force acting.
But the equilibrium is when forces are balanced and the object does not change its motion. Normal force is the force that surfaces exert to prevent solid objects from passing through each other. This is important regarding the first law because the rocket stays sitting on the launch pad and until you pull the string is stays in its state of rest. Objects an rest on earth with a constant force of gravity because whatever the object is rest on is exerting a force on the object.
Newton's 2nd law is “the force on an object is equal to its mass times its acceleration.” (a=F/m) The force on an object is the push or pull with mass and it causes it to change its velocity. One way to measure force is with newtons. A newton is a force that can be used to accelerate one kilogram of mass one meter per second squared. Friction, drag, and weight are all types of force. Friction resists motion when it comes in contact with another surface. Drag is when an object interacts and has contact with a solid body with a fluid. While weight is the measurement of the heaviness of an object and the force of gravity on an object. Although mass is not a force it is used in the equation (a=F/m). Mass is a measure of inertia the greater the mass of an object, the smaller the change produced by an applied force.
Newton's 3rd law is “when two objects interact, they apply forces to each other of equal magnitude and opposite direction.” Some examples are when you are swimming you are pushing against the water you are being pushed forward by the water. Aswell as a book resting on a table the weight of the book is acting in the downward direction on the table and the table is exerting an equal force upward. These are both examples where objects are exerting force on each other. This is know as a system.
This September in math we learned about quadratic equations, representing velocity using vectors. Quadratic equations are equations where the largest exponent above a variable is 2. We can use these quadratic equations to help figuring out different aspects of our rocket including initial velocity, time, and height. We can define a quadratic function as y+x2. The position represented on the height vs time graph can be represented by a point where the rocket's height is given time. The velocity on the graph can be represented because the slope is the velocity. The acceleration is represented because acceleration is the curve itself and represents a change slope or changing velocity. A quadratic function can be represented as h(t) = , g represents the acceleration from gravity, and represents the initial velocity, and it represents the object's initial height. Velocity is the direction of the movement of an object. While acceleration is the rate of change of velocity. G represents gravity.
This semester in physics we focused on Newton's 3 laws of motion. Newton's first law is “An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.” This law includes inertia, net force and normal force. Inertia is the property of matter by which it continues in its existing state of motion unless it is changed by an external force. The net force results in a change in motion. The force that creates all of the pushing and pulling forces that are actually applied to an item is known as the net force. Which results in an object that will accelerate in the direction of the net force if the forces pushing and tugging on it are out of balance, or if there is a net force acting.
But the equilibrium is when forces are balanced and the object does not change its motion. Normal force is the force that surfaces exert to prevent solid objects from passing through each other. This is important regarding the first law because the rocket stays sitting on the launch pad and until you pull the string is stays in its state of rest. Objects an rest on earth with a constant force of gravity because whatever the object is rest on is exerting a force on the object.
Newton's 2nd law is “the force on an object is equal to its mass times its acceleration.” (a=F/m) The force on an object is the push or pull with mass and it causes it to change its velocity. One way to measure force is with newtons. A newton is a force that can be used to accelerate one kilogram of mass one meter per second squared. Friction, drag, and weight are all types of force. Friction resists motion when it comes in contact with another surface. Drag is when an object interacts and has contact with a solid body with a fluid. While weight is the measurement of the heaviness of an object and the force of gravity on an object. Although mass is not a force it is used in the equation (a=F/m). Mass is a measure of inertia the greater the mass of an object, the smaller the change produced by an applied force.
Newton's 3rd law is “when two objects interact, they apply forces to each other of equal magnitude and opposite direction.” Some examples are when you are swimming you are pushing against the water you are being pushed forward by the water. Aswell as a book resting on a table the weight of the book is acting in the downward direction on the table and the table is exerting an equal force upward. These are both examples where objects are exerting force on each other. This is know as a system.
Calculation:
Using the math we learned in class we can calculate our rocket’s statistics. These being the Max height, Initial velocity, and Theoretical flight time. With what Julian taught us, we can find out the force of gravity, thrust, and descent velocity. My group didn't have a video so we have to do certain math differently.
What we know:
The angle measurer was taken 60 m back from the launcher.
The angle was 54 degrees.
The Altitude of the angle measurer above ground is 4.75ft
Max Height:
Step 1: The equation of best fit is tangent because we are using the opposite and the adjacent sides.
tan()=oppadj
Step 2: Fill out what we know
tan(54)=x60
Step 3: Get x by itself
60tan(54)=x
86.68=x
Step 4: Add the height of the angle measured
Height above ground:
86.68 + 1.5 = 88.18
After launching our rocket we already know our max height but using this math we can see how correct our alternator really is. In order to find the max height of our rocket we need to use SOH CAH TOA. In this case we will be using TAN. The first step is to make a triangle and label with opposite, adjacent, and hypotenuse. With this situation we are trying to find the opposite. Since we are using tan we can using the equation tan()=opp adj and with what we know we can plug the number in so it looks like tan(54)=x60. After we solve this we get 86.68 for our max height. But since the rockets starting is 1.5 we need to add it to our total. Our final answer is 88.18.
Initial velocity:
h(t) = height given time
G= gravity
Vo=initial velocity
Ho= starting height
Instead of using v0= distance/time to find the Initial velocity we can use the equation h(t) = -½ gt2 + vot + 0.3. We using this equation because we didn't have a video.
We then can plug in our numbers.
Force of Gravity:
To find my rockets force of gravity you need to know all objects on (or near) Earth's surface accelerate at the same rate: 9.81 m/s. now we can calculate the force of gravity acting on objects of different mass by using the Force-Mass equation from Newton's second law of motion. For this section we need to find out the mass of the rocket with and without water. When we weighed our rocket with water it weighed 1.023 kg and without out water our rocket weighed 0.176 kg. To find the force of gravity with water we plug these number into the equation f gfull= mg= 1.023kg*(9.81m/s2) and get 10.03kg m/s2. To find the force of gravity without water we plug it into the equation
Fg emty=mg=.17gkg * 9.81 m/s2 and get 7.45 m/s2.
Since acceleration is due to the Net force acting on tan object to force the rocket encountered are gravity, air friction and drag.
Thrust
Formulas
a=Δ v/t= (v0-0)/t
F=ma
Force- Mass Equation
F= ma
Average acceleration equation:
a=Δ v/t
Our next step was to figure out our rocket's thrust. In order to calculate the force of thrust on the rocket, we need to identify the average rate acceleration of the rocket during take off. Once we find this we can find the net force acting on the rocket by multiplying it by mass. Next we can account for the force of gravity as apart of this net force to calculate the force of thrust. Next we will need to add the force of gravity and the netforce.
The first step we did was took 3/30 to get .1 and plugged that into our equation a=v0/t to get 41.51/.1 this equals 415 this means our rocket had a thrust force of 41.5. nExt we need to calculate the netforce Fnet =ma= 42.5
3/30 comes from there being 30 frames per second and 3 frames our rocket was traveling.
Theoretical Flight time
Equation
When finding the theoretical flight time we were given an equation and after plugging in A, B, C into the formula we were able to get our final answer 8.31. We also had to incorporated the graph which our time of max height we found was 4.1 seconds.
Decent velocity
For our descent velocity we are given our height of 86.68m we have to divide that by our descent speed which is 6m/s. After doing this calculation we found our decent velocity is 14.44 seconds till it reaches ground level.
86.68/6ms= 14.44
What we know:
The angle measurer was taken 60 m back from the launcher.
The angle was 54 degrees.
The Altitude of the angle measurer above ground is 4.75ft
Max Height:
Step 1: The equation of best fit is tangent because we are using the opposite and the adjacent sides.
tan()=oppadj
Step 2: Fill out what we know
tan(54)=x60
Step 3: Get x by itself
60tan(54)=x
86.68=x
Step 4: Add the height of the angle measured
Height above ground:
86.68 + 1.5 = 88.18
After launching our rocket we already know our max height but using this math we can see how correct our alternator really is. In order to find the max height of our rocket we need to use SOH CAH TOA. In this case we will be using TAN. The first step is to make a triangle and label with opposite, adjacent, and hypotenuse. With this situation we are trying to find the opposite. Since we are using tan we can using the equation tan()=opp adj and with what we know we can plug the number in so it looks like tan(54)=x60. After we solve this we get 86.68 for our max height. But since the rockets starting is 1.5 we need to add it to our total. Our final answer is 88.18.
Initial velocity:
h(t) = height given time
G= gravity
Vo=initial velocity
Ho= starting height
Instead of using v0= distance/time to find the Initial velocity we can use the equation h(t) = -½ gt2 + vot + 0.3. We using this equation because we didn't have a video.
We then can plug in our numbers.
Force of Gravity:
To find my rockets force of gravity you need to know all objects on (or near) Earth's surface accelerate at the same rate: 9.81 m/s. now we can calculate the force of gravity acting on objects of different mass by using the Force-Mass equation from Newton's second law of motion. For this section we need to find out the mass of the rocket with and without water. When we weighed our rocket with water it weighed 1.023 kg and without out water our rocket weighed 0.176 kg. To find the force of gravity with water we plug these number into the equation f gfull= mg= 1.023kg*(9.81m/s2) and get 10.03kg m/s2. To find the force of gravity without water we plug it into the equation
Fg emty=mg=.17gkg * 9.81 m/s2 and get 7.45 m/s2.
Since acceleration is due to the Net force acting on tan object to force the rocket encountered are gravity, air friction and drag.
Thrust
Formulas
a=Δ v/t= (v0-0)/t
F=ma
Force- Mass Equation
F= ma
Average acceleration equation:
a=Δ v/t
Our next step was to figure out our rocket's thrust. In order to calculate the force of thrust on the rocket, we need to identify the average rate acceleration of the rocket during take off. Once we find this we can find the net force acting on the rocket by multiplying it by mass. Next we can account for the force of gravity as apart of this net force to calculate the force of thrust. Next we will need to add the force of gravity and the netforce.
The first step we did was took 3/30 to get .1 and plugged that into our equation a=v0/t to get 41.51/.1 this equals 415 this means our rocket had a thrust force of 41.5. nExt we need to calculate the netforce Fnet =ma= 42.5
3/30 comes from there being 30 frames per second and 3 frames our rocket was traveling.
Theoretical Flight time
Equation
When finding the theoretical flight time we were given an equation and after plugging in A, B, C into the formula we were able to get our final answer 8.31. We also had to incorporated the graph which our time of max height we found was 4.1 seconds.
Decent velocity
For our descent velocity we are given our height of 86.68m we have to divide that by our descent speed which is 6m/s. After doing this calculation we found our decent velocity is 14.44 seconds till it reaches ground level.
86.68/6ms= 14.44
Reflection:
Leadership and Teamwork:
During this project me and my partners worked well together. Each day we showed up to get our rocket done. During this project we didn't have any conflicts. We didn't have any conflicts because we all were doing work and never were not doing anything to help. When working with this group we all communicated if we needed help or wanted anything to change. I was a leader in this group because If a group member wasn't doing anything to help I would encourage them to do so. I was also a leader by taking initiative and making our blueprint. I was a follower when others had ideas and if they asked me to do something. For example when I helped Alex attach the nose fin, and we both made the parachute. During this project each person has their strengths and weaknesses. With that we assigned the people things they would be good at, and did not give them something they couldn't do. For example throughout the project I let Aiden help me with attaching the fins and little things.
During this project me and my partners worked well together. Each day we showed up to get our rocket done. During this project we didn't have any conflicts. We didn't have any conflicts because we all were doing work and never were not doing anything to help. When working with this group we all communicated if we needed help or wanted anything to change. I was a leader in this group because If a group member wasn't doing anything to help I would encourage them to do so. I was also a leader by taking initiative and making our blueprint. I was a follower when others had ideas and if they asked me to do something. For example when I helped Alex attach the nose fin, and we both made the parachute. During this project each person has their strengths and weaknesses. With that we assigned the people things they would be good at, and did not give them something they couldn't do. For example throughout the project I let Aiden help me with attaching the fins and little things.