cover letter
For this unit of Math 10 we had an exhibition for rockets. Our goal for this was to successfully build launchable rockets made from plastic bottles. We worked with graphing quadratics, factoring and completing the square. With these we were able to make all our calculations, using factoring we were able to solve our equations step by step. Completing the square taught us how to solve our equations without having to do a bunch of long steps allowing us to get our answer quicker. Finally graphing taught us how to simplify our functions and graph them. Thus giving us all our calculations for our rockets.
Calculations
Time of Max height
In order to find our max height we had to record our rockets being launched, then you need to upload to the computer and count how many frames per second. We did ours on an iphone which shoots 30 frames per second, then from there we calculated the time of max height by counting how many frames it took to get to max height. After , we then divided the number of frames by 30. We had 53 frames so you would divide 53 by 30 which equals 1.76 seconds.
Max Height
To calculate the max height you have to get the angle of your rocket, for us it would be 25. Next you use the formula tangent and plug the angle into the equation. Tan (25) y/200. Our answer was y = 93.2 ft. the new equation would be 93.2 + 4.75 which gives us 98.0 ft which was out max height.
Initial Velocity
To calculate initial velocity we used the formula h (t) = -12 (g) (t)2+ V0(t) + y0
We plugged in what we already knew, Vo = Initial Velocity, g = Gravity, and t = Time, y0 = starting height. Our initial velocity is unknown, our time is 1.76 seconds. Our gravity is 32 ft/s^2. Our starting height is 1.5. Our max height is 98.0. Using our formula and plugging in our calculations (time, gravity. Starting height, and max height) using algebra we solved for initial velocity which came out to 82.92.
Theoretical flight time
To calculate the theoretical flight time we used the formula for height at any given time. h(t)= yo+Vo(t)-12(g)(t2) and the quadratic formula
-bb2-4ac
X = 2a
For the formula of height for any given time, we plugged in all of our numbers
h(t) = -16t ^2+ 82.92t + 1.5
Using the quadratic formula we found our a,b, and c and plugged it into the formula.
-82.9282.922-4(-16)(1.5)\
X = 2(-16)
When we solve the quadratic formula we got x = 5.20 seconds which is our theoretical flight time.
In order to find our max height we had to record our rockets being launched, then you need to upload to the computer and count how many frames per second. We did ours on an iphone which shoots 30 frames per second, then from there we calculated the time of max height by counting how many frames it took to get to max height. After , we then divided the number of frames by 30. We had 53 frames so you would divide 53 by 30 which equals 1.76 seconds.
Max Height
To calculate the max height you have to get the angle of your rocket, for us it would be 25. Next you use the formula tangent and plug the angle into the equation. Tan (25) y/200. Our answer was y = 93.2 ft. the new equation would be 93.2 + 4.75 which gives us 98.0 ft which was out max height.
Initial Velocity
To calculate initial velocity we used the formula h (t) = -12 (g) (t)2+ V0(t) + y0
We plugged in what we already knew, Vo = Initial Velocity, g = Gravity, and t = Time, y0 = starting height. Our initial velocity is unknown, our time is 1.76 seconds. Our gravity is 32 ft/s^2. Our starting height is 1.5. Our max height is 98.0. Using our formula and plugging in our calculations (time, gravity. Starting height, and max height) using algebra we solved for initial velocity which came out to 82.92.
Theoretical flight time
To calculate the theoretical flight time we used the formula for height at any given time. h(t)= yo+Vo(t)-12(g)(t2) and the quadratic formula
-bb2-4ac
X = 2a
For the formula of height for any given time, we plugged in all of our numbers
h(t) = -16t ^2+ 82.92t + 1.5
Using the quadratic formula we found our a,b, and c and plugged it into the formula.
-82.9282.922-4(-16)(1.5)\
X = 2(-16)
When we solve the quadratic formula we got x = 5.20 seconds which is our theoretical flight time.
Blueprint |
rocket video |
Reflection
A challenge I encountered during the rocket project was rebuilding our rocket several times because certain opponents in our rocket didn't work the way we wanted them to. An example of this was when we had to remake our fins because they were too tiny so they didn't create enough drag for our rocket. We went through a long process of trial and error with our fins but we never stopped trying to make the fins as best as they could be. I navigated through these challenges by not giving up and being perseverant. It was also really useful to have a partner in this rocket project who had a high spirit and was determined to make our rocket good.
One of our biggest successes was having a parachute that was actually deployed. It was so encouraging seeing our parachute deploy and gave me a lot of motivation to keep on working hard. We spent a lot of time and effort trying to make our parachute work and had to compromise a lot. Asking teachers and students for help was really useful. I would tell next year's sophomores to not be scared to ask for help, I am incredibly grateful for everyone who helped us out and gave us encouragement. If it wasn't for the help that Ande and Madi gave us, our rocket wouldn't have been as good as it was.
The turning point for me in this project was also our parachute because seeing it deploy was the first time throughout the entire project that I got excited. To be completely honest, I wasn't excited about the rocket project at all. Math and science are subjects that I'm particularly interested in and I originally planned to do the bare minimum. After seeing our parachute deploy, I was immediately encouraged to make our rocket as good as it could possibly be. It was truly such an amazing feeling seeing our rocket partially work for the first time. Although the parachute deployed, there were many other aspects of our rocket that didn't work out well but I gained the motivation to fix those aspects.
I learned that collaboration and comunication is super important in group projects. My partner and i had some disagreements but we never let them get in the way between us. I learned that it is very impotant to not take those small little disagreements seriously when you are doing prejects like this. I will appply this in future projeccts and life by voicing my opinion more often but also listening to other peoples opinions. Without communication and collaboration, my partner and i wouldnt have had a succesful rocket.
If i were to do this project again, i would do more research and actually look at the example rockets Ande and Madi gave us. The process of making our rocket would have been so much easier and less stressful if i took the time to look at them. A huge lesson i learned is that it is very important to listen to your teachers, i originally thought that the examples were useless to me and that it would have been a waste of time to look at them. If i was able to go back in time and have a do over, i would have listened to my teachers from the beginning.
One of our biggest successes was having a parachute that was actually deployed. It was so encouraging seeing our parachute deploy and gave me a lot of motivation to keep on working hard. We spent a lot of time and effort trying to make our parachute work and had to compromise a lot. Asking teachers and students for help was really useful. I would tell next year's sophomores to not be scared to ask for help, I am incredibly grateful for everyone who helped us out and gave us encouragement. If it wasn't for the help that Ande and Madi gave us, our rocket wouldn't have been as good as it was.
The turning point for me in this project was also our parachute because seeing it deploy was the first time throughout the entire project that I got excited. To be completely honest, I wasn't excited about the rocket project at all. Math and science are subjects that I'm particularly interested in and I originally planned to do the bare minimum. After seeing our parachute deploy, I was immediately encouraged to make our rocket as good as it could possibly be. It was truly such an amazing feeling seeing our rocket partially work for the first time. Although the parachute deployed, there were many other aspects of our rocket that didn't work out well but I gained the motivation to fix those aspects.
I learned that collaboration and comunication is super important in group projects. My partner and i had some disagreements but we never let them get in the way between us. I learned that it is very impotant to not take those small little disagreements seriously when you are doing prejects like this. I will appply this in future projeccts and life by voicing my opinion more often but also listening to other peoples opinions. Without communication and collaboration, my partner and i wouldnt have had a succesful rocket.
If i were to do this project again, i would do more research and actually look at the example rockets Ande and Madi gave us. The process of making our rocket would have been so much easier and less stressful if i took the time to look at them. A huge lesson i learned is that it is very important to listen to your teachers, i originally thought that the examples were useless to me and that it would have been a waste of time to look at them. If i was able to go back in time and have a do over, i would have listened to my teachers from the beginning.