Honors Math: CS50x
For honors math, we were tasked to work through the next problem set in the CS50 online course. These problem sets were a lot more difficult than what we started out working on earlier in the year. These were considered the "Hacker Edition" problem sets, which basically means there is no where to go where people can help you. These problem sets brought us back to our early days as computer coders, where we knew nothing about it and were just trying to get the computer to say "hello world" back to us. We had to do a lot of research and patchwork to even get it to compile. We worked primarily with pseudo-code to try and figure out the process to solve the problem rather than getting caught up on the correct syntax. Together we were able to figure out most of the equations but not all of them, I feel if we worked more on the problem set, that we could figure out the solution to all of them.
Over the past two years I have been learning how to code primarily with C/C++ but also a little bit earlier on with Python. They have their similarities and differences but the concept is the same, and when I firsted started playing around with coding, I knew what I wanted to do. Coding has caused me a lot of headaches and frustration in the past, but it is extremely rewarding when you get your code to work. This has lead me into trying to get into the industry. I stick with coding because I know that one day I will not be getting caught up on little problems, I will get to a point where it would be quick to write code and I could make great things with it.
Over the past two years I have been learning how to code primarily with C/C++ but also a little bit earlier on with Python. They have their similarities and differences but the concept is the same, and when I firsted started playing around with coding, I knew what I wanted to do. Coding has caused me a lot of headaches and frustration in the past, but it is extremely rewarding when you get your code to work. This has lead me into trying to get into the industry. I stick with coding because I know that one day I will not be getting caught up on little problems, I will get to a point where it would be quick to write code and I could make great things with it.
The Ferris Wheel Problem
We measured out each length and angle in our notebooks before we started to make sure that we had the correct scale
for each of the lengths of the sides of the Ferris wheel.
for each of the lengths of the sides of the Ferris wheel.
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These are the pages of notes we had in planning the build of our ferris wheel. We had to find out the speed of the ferris wheel and height off of the ground to build it correctly. We also planned out how we would layer the popsicle sticks so that the ferris wheel wouldn't be lopsided.
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In order to figure out when to drop the diver from the wheel and to have them land in the water of the cart, we need to use the last few formulas and a couple new ones.
First, we need to know the horizontal position of the cart on the track. We established that the cart starts moving as soon as the Ferris wheel moves and that the cart moves at a constant speed of 15 ft/second. The cart's starting position is 240 feet from the center of the wheel. To calculate the position of the cart, while keeping in mind how many seconds have passed, we used this formula: |
The capital T in this diagram is actually feet, in the horizontal position. Essentially, this formula will allow us to place the cart at any position after the wheel starts moving. This helps in determining the drop point.
The next thing that we need to keep in mind is the horizontal position of the diver and the platform. In order to drop them at an appropriate place, the horizontal position of the cart and the diver need to be practically the same (with 8 feet of leeway, because the cart is 8 feet long). We discerned that the formula to find out the horizontal position of the diver is almost exactly the same as the formula we use to find the height of the diver, with a few minor changes. |
This is the formula we used to find the horizontal position of the diver. We used cosine because rather than trying to find the height of the diver, we we're trying to find their horizontal position relative to the center.
After putting these two formulas together, we can begin to input seconds and decide at what point the diver should be dropped from. During class, we made it clear that if the diver was dropped 10 seconds after the wheel and the cart have begun moving, that the diver would die because they were not within the 8 foot parameters of the cart. But her landing spot was only about 2 feet off from the cart, which means the actual time must be something close to 10 seconds. |
In the beginning, we established the variables in the problem, so that we could start breaking the problem down. We scaled it down to make it easier to build, we made the scale 1:10. Once we established all of the variables, we started to solve each problem, eventually getting to a point where we could reach the solution. I feel my partner and I did very well in the planning stage and in the process of building it. We were very precise with our plans and made sure that when we built it the lengths widths and even the angles were exact to the plans. Ours came out precisely to scale and it did a great job at recreating the problem.
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In this problem set, we were given a scenario in which there are two people on a Ferris wheel. One of the performers is holding the other by the ankles and, while the wheel is spinning, tries to drop his partner into a moving cart of water that is on a track below the wheel (figure 1). We want to determine the right time and height to drop the diver from. We needed to recreate the problem three dimensionally to get a better understanding of the problem and to really solve the problem.
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