High Dive
In this problem, a circus group is attempting to drop a diver from the edge of a moving Ferris Wheel. He is dropped into a moving cart of water under the Ferris Wheel. The person dropping the diver need to know at the exact moment to drop the diver as to not create any damage. The answer we are trying to find, is in terms of time. PROCESS: Using our creativity and math skills, we need to create a scale model of the cart and Ferris Wheel. Our first step in constructing this was to identify all variables and assumptions. The variables identified where the following: Ferris Wheel height, wheel radius, cart speed, wheel speed, wheel circumference, wheel rotation speed, and the distance from center of the wheel to the ground and cart. We were given the assumption that there will be no air resistance, friction and everything is moving at a constant speed. Also, both the diver and the cart will be seen as points in a graph. |
For my group's Ferris wheel our scale was 1 inch = 9.75 feet. We got this by dividing 100 ( the diameter of the wheel) and 10.25 ( The diameter of our wheel) to the scale.
SLIDE SHOW OF MODEL:
We used the model as a way to try out assumptions. We based of our calculations to help us decide how much the cart should move every second while the diver rotates.
VERTICAL POSITION PROCESS:
We were able to find the speed by dividing 360 (the degrees inside a circle) by 40 (the seconds taken for the wheel to do a full rotation). We continue with using the sine function. This is due to the fact that we are solving for the opposite side of the triangle; the length of the time in the Ferris wheel to the center. By doing this, we come up with the equation y=50*sin(9t)+65.
AMPLITUDE:
FINAL GRAPH:
![Picture](/uploads/7/8/6/7/78679274/1476414547.png?250)
The amplitude of our graph is 50 because it is the same as the circles radius.
The period of our graph would be 40, this is because it takes 40 seconds to complete a full revolution.
The vertical shift of our graph would be 65 because that is the constant variable. If we make this number smaller, the graph will shift down. If we make it bigger it will move up.
AIR TIME
To find the air time of the diver we had to go through several different processes, finding different formulas to create the final air time formula which is time is equal to the square root of height divided by sixteen.
To find the air time of the diver we had to go through several different processes, finding different formulas to create the final air time formula which is time is equal to the square root of height divided by sixteen.
HORIZONTAL POSITION
CART POSITION
FINAL FORMULA
To find the final answer, we have to combine all equations found. This will be helpful in determining at what time should the diver be dropped in order to survive. We first startd with the guess and check method which consists of plugging in certain times. This would be helpful in knowing if the time chosen was right. We determined this by comparing the x-coordinate of the cart with the x-coordinate of the diver considering air time in the process. The formula below is the combination of everything learned.
To find the final answer, we have to combine all equations found. This will be helpful in determining at what time should the diver be dropped in order to survive. We first startd with the guess and check method which consists of plugging in certain times. This would be helpful in knowing if the time chosen was right. We determined this by comparing the x-coordinate of the cart with the x-coordinate of the diver considering air time in the process. The formula below is the combination of everything learned.
FINAL ANSWER
To find the solution for the diver problem, we first had to create a formula combining all of the formulas that we used to find the horizontal position of the cart, the vertical position of the diver, the horizontal position of the diver, and his fall time. After doing that we separated the two sides of the equation and graphed them (since the solution to two functions when graphed are where they intersect). Finally, we found that the functions intersected at 12.283 on the x axis. So the diver will survive when he's released at 12.283 seconds. (If you plug this number in for the "t" in the equation, you will get 12.283=12.283.
PROBLEM EVALUATION
Throughout this problem, there was alot of thinking and prcticing being involved. Personally, I didnt really enjoy this problem. This is because I thought it was too much time spent in only one problem. But, I enjoyed the opporunity to grasp and play with it.
SELF EVALUATION
If I was to give myself a grade over the past 10 weeks, I would give myself and -A. This is because I feel that there are some aspects I could have worked harder on.
Throughout this problem, there was alot of thinking and prcticing being involved. Personally, I didnt really enjoy this problem. This is because I thought it was too much time spent in only one problem. But, I enjoyed the opporunity to grasp and play with it.
SELF EVALUATION
If I was to give myself a grade over the past 10 weeks, I would give myself and -A. This is because I feel that there are some aspects I could have worked harder on.