Problem and PRocess
"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, as shown in the picture on the right. We have to determine when, exactly, the performer can be dropped so that she lands in the moving cart."
We started out the problem by listing variables and assumptions. To help us visualize the problem we made scale models of the Ferris wheel from the problem.
After we finished building the models of the Ferris wheels we had to find a way to calculate how long it would take the diver to fall from the platform. Because this variable depends on the height of the platform we had to find a way to calculate the height of the diver's platform at any time. We came up with this equation: y={[50(sin9x)]+65} where y is height from the ground and x is time after start. This equation assumes that the wheel moves at nine degrees per second and starts at the 3 o'clock position.
The next step was to find a way to calculate the fall time of the diver as she/he fell from any position on the Ferris wheel. To find this equation we used the example of a volleyball being dropped from the height of the ceiling. If we know the time, how can we find the height that it fell from? |
We found the equation h=16t^2. By rearranging the equation we were able to find a way to calculate the fall time of the diver. By combining the two equations that we found (and factoring in the height of the cart) we made an equation that could tell us the diver's fall time at any time after the wheel started moving.
The next step was to find an equation that could calculate the position of the diver on the x-axis at any time and an equation to calculate the position of the cart at any time. All three equations are shown below.
ASSESSMENT and Reflection
If I were to give myself a grade for all the work that I've done in math over the past 10 weeks, it would be an A-. I've been invested in finding a solution to the circus act problem and have made an effort to engage with my peers during class. Towards the end of the project, however, I lost interest in the problem and withdrew from my classmates.
I think that the problem moved painfully slow, which made it hard to stay engaged. I found myself coming to class each day only to be presented with a question I had found the answer to the previous day. In contrast to this, I really enjoyed making the video because I felt like I was learning something new and interesting and could work at my own pace and level.
I think that the problem moved painfully slow, which made it hard to stay engaged. I found myself coming to class each day only to be presented with a question I had found the answer to the previous day. In contrast to this, I really enjoyed making the video because I felt like I was learning something new and interesting and could work at my own pace and level.