Problem Statement: To kick off the year we we faced with 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. |
Showing the math:
Math showing calculations of how you determined scale .
Math showing calculations of how you determined scale .
The Process:
Overview:
The "Circus Act" Problem was about finding a range of time where the diver could land inside the cart without being splattered on the track. The diver would be jumping off a Ferris Wheel while the wheel is moving counter clockwise and the cart underneath is moving at the same rate to the right.Our task was to figure out when will the wheel and cart matchup enough for the diver to land inside the cart.
Step One: To start off the problem, we had to come up with the constants of the wheel and the cart. These constants included rotational speed for the wheel, movement speed of the cart, and acceleration of the diver. From these constants we were able to decide the four main parts of the problem. These 4 parts are; vertical position of the diver, horizontal position of the diver, air time, and cart position.
Step Two: Once we figured out what our main focuses were we decided to start of with find out what our platform's height at any time. We knew that the radius of our Ferris Wheel is 50 . height of the wheel was 65 feet in. In any right triangle, the sin of an angle x is the length of the opposite side (O) divided by the length of the hypotenuse (H). So knowing this we were able to get “H = 50sin (9T) + 65”. H stands for the fact that we are trying to find that platform's height at any time, we know that from the certain of the wheel is to the platform is 50 feet, 9 is the degrees between the platform and the next possible platform height, and lastly the 65 is how tall the wheel is from the center to the track that the cart is on.
Step Three: Now that we are able to find the position of the diver at any time, we need to calculate the airtime of the diver when jumping from the platform. To start off we used the height from the starting position to get a baseline. We know that the speed of acceleration is 32 ft/ per second. We also know that the diver is going to fall 57 feet to the cart. If we plot the time on the y axis and the speed on the x axis we can plot a line. This line describes the path of the diver. We know the area below a line is the distance traveled. With all of this information we can solve for the air time. If we take the starting height and then divide it by the final speed divided by two,
Step Four:
The horizontal position of the diver is using cos. the cos of an angle is the length of the adjacent side (A) divided by the length of the hypotenuse (H).
Since we had two of the angels [ say what the angles are ] the equation we came you with to help us find the horizontal position was cos(9T)50.
Step Five:
To solve for the position of the cart at any time we need to come up with a formula. We know that the starting position of the cart is -240 feet in relation to the center of the ferris wheel. We also know that the cart moves 15 feet every second. This means that the cart is 15 feet closer to 0 every second. We can combine all of this information to come up with the formula
-240 + (15 x t)
Step Six: In conclusion we need to take all of our information and try to find what the survival time of when the diver will land in the cart. Our was 8 feet long so this meant that our diver could fall at different points inside of the cart.
Overview:
The "Circus Act" Problem was about finding a range of time where the diver could land inside the cart without being splattered on the track. The diver would be jumping off a Ferris Wheel while the wheel is moving counter clockwise and the cart underneath is moving at the same rate to the right.Our task was to figure out when will the wheel and cart matchup enough for the diver to land inside the cart.
Step One: To start off the problem, we had to come up with the constants of the wheel and the cart. These constants included rotational speed for the wheel, movement speed of the cart, and acceleration of the diver. From these constants we were able to decide the four main parts of the problem. These 4 parts are; vertical position of the diver, horizontal position of the diver, air time, and cart position.
Step Two: Once we figured out what our main focuses were we decided to start of with find out what our platform's height at any time. We knew that the radius of our Ferris Wheel is 50 . height of the wheel was 65 feet in. In any right triangle, the sin of an angle x is the length of the opposite side (O) divided by the length of the hypotenuse (H). So knowing this we were able to get “H = 50sin (9T) + 65”. H stands for the fact that we are trying to find that platform's height at any time, we know that from the certain of the wheel is to the platform is 50 feet, 9 is the degrees between the platform and the next possible platform height, and lastly the 65 is how tall the wheel is from the center to the track that the cart is on.
Step Three: Now that we are able to find the position of the diver at any time, we need to calculate the airtime of the diver when jumping from the platform. To start off we used the height from the starting position to get a baseline. We know that the speed of acceleration is 32 ft/ per second. We also know that the diver is going to fall 57 feet to the cart. If we plot the time on the y axis and the speed on the x axis we can plot a line. This line describes the path of the diver. We know the area below a line is the distance traveled. With all of this information we can solve for the air time. If we take the starting height and then divide it by the final speed divided by two,
Step Four:
The horizontal position of the diver is using cos. the cos of an angle is the length of the adjacent side (A) divided by the length of the hypotenuse (H).
Since we had two of the angels [ say what the angles are ] the equation we came you with to help us find the horizontal position was cos(9T)50.
Step Five:
To solve for the position of the cart at any time we need to come up with a formula. We know that the starting position of the cart is -240 feet in relation to the center of the ferris wheel. We also know that the cart moves 15 feet every second. This means that the cart is 15 feet closer to 0 every second. We can combine all of this information to come up with the formula
-240 + (15 x t)
Step Six: In conclusion we need to take all of our information and try to find what the survival time of when the diver will land in the cart. Our was 8 feet long so this meant that our diver could fall at different points inside of the cart.
- If the diver landed at the front of the cart he would land at 12. 293
- If the diver landed at the front of the cart he would land at 12.5 back cart
- If the diver landed at the front of the cart he would land at 11.45 middle cart
Things I have learned:
3 Big things that I have learned from others in this unit. Is one I should not be afraid to ask questions. While working on this unit there were moments during this unit when I did not know what was going on and I did want to ask questions because, I was afraid of being wrong. Then the longer we went on with the unit I knew that sitting there lost was not going to help. So I stared asking clarifying questions that will help me solve the problem. Another thing that I learned was to ask my peers for help, if I did not know something then there was a high probability that my peers did. By me asking them questions I was able to understand the problem better. Lastly what I learned from others in this unit is that making mistakes is okay. When my peers and I would make mistakes we would get discouraged and want to quit. We knew that if we were to quit then we would never get anything done and me our "deadlines". So we had to push through that can't do this mindset and figure out what we can do. This was we are able to figure out the correct way to solve this unit. All in all working on The "Circus Act" Problem gave me a new way to look at math by applying it to this problem.
3 Big things that I have learned from others in this unit. Is one I should not be afraid to ask questions. While working on this unit there were moments during this unit when I did not know what was going on and I did want to ask questions because, I was afraid of being wrong. Then the longer we went on with the unit I knew that sitting there lost was not going to help. So I stared asking clarifying questions that will help me solve the problem. Another thing that I learned was to ask my peers for help, if I did not know something then there was a high probability that my peers did. By me asking them questions I was able to understand the problem better. Lastly what I learned from others in this unit is that making mistakes is okay. When my peers and I would make mistakes we would get discouraged and want to quit. We knew that if we were to quit then we would never get anything done and me our "deadlines". So we had to push through that can't do this mindset and figure out what we can do. This was we are able to figure out the correct way to solve this unit. All in all working on The "Circus Act" Problem gave me a new way to look at math by applying it to this problem.