Problem Statement:
In the "circus act" problem, a circus performer is dropped from a moving Ferris Wheel into a cart of water that is moving below the Ferris Wheel. We have to determine when, exactly, the performer can be dropped so that she lands in the moving cart.
process:
When we first started the problem we had to figure out some of the kinks of the problem. We concluded that the Ferris Wheel will take 40 seconds to complete a full turn, the diver started at the 3 o'clock position, the cart will move at 15 feet per second, no wind resistance, the cart will start -240 feet away from the Ferris wheel, and that the fall time is dependent on this constant, the diver will fall 32 feet per second squared or 32ft/secxsec.
We then had to create an equation to help us solve the fall time, and here it is.
We then had to create an equation to help us solve the fall time, and here it is.
Then we had to calculate the horizontal position of the diver. We needed to do this in order to help us calculate the fall time more precisely. Given that the diver starts at the 3 o'clock position, we came to this equation to get the horizontal position of the diver.
After we found this equation, we had to calculate for the distance that the cart has traveled. To find this answer, all we had to do is just input the amount of time the wheel has spun and multiply it by 15. We multiply the time by 15 because the cart is moving at a constant rate of 15 feet per sec. Now that we knew this we thought we could simplify it even further. WE decided to combine the fall time and distance of the cart into one whole equation.
Now that this equation is made we just calculate this and the horizontal position to get the exact point of where the diver will hit the top of the cart.so now that we have this figured out we just now insert certain times for the Ferris Wheel for the diver. We have figured out a great time down to the thousand of a second.
In this picture, FT: stands for fall time, H.C: stands for position of cart, and H.D: stands for the position of the diver relative to the top of the cart. The diver survives by .001 of a second.
Other Peoples process:
I learned many things from this project, the first big thing I learned was the equation/solution to solving for a perfect triangle, the 30,45,90 degree triangle. I watched some one bring up the equation and input the numbers and then solved for the distances of the triangle. The second big thing that learned from some one was the ability to combine equations, at first I was told to combine/make a combination of the fall time and the carts position. The last big thing I learned from some one else was inputing the correct numbers into the correct equation. They taught that the time was solely dependent on the amount of time the diver was on the Ferris Wheel.
Solution:
RSAVideo.mov |
Self- ASSESSMENT:
This was a long and extensive project that took us around 10 weeks to complete. During these weeks I worked as best as I could. I did this by being engaged in the conversations, asking questions, solving the questions given, communicating with peers, and just trying my best to get the best possible answer for this problem. If I were to give myself a grad I believe I should get is a A- (90%) or an A (95%),
Problem Evaluation:
For this project i think that it kept me entertained/engaged the entire time. During this problem,it pushed me to learn new methods for solving certain triangles, finding the rate of falling, an combining different equation into one to complete the problem. I think that the most I got out of this was being able to learn new things that were challenging. However I made it fun for myself by trying to solve/understand them.