The reason I'm looking at the cable car is because the slopes for this are way different than those found associated with American roads. The maximum for American roads is 6 percent or up six feet for every 100 feet.
The trolley or cable car makes a stop at the castle level, at the general view where you change trolleys or the top. Based on what I could see, it looks like the slope for the first two parts is about 22 %. The last part, the wooden cable car had an even steeper slope. It began at 22%, moved to 28% and ended up at a 40%. Going down the hill, looking back up, I could actually see the curve in the hill as the slope increased.
This opens up some interesting types of open possibilities for the math class. Think about telling the students there is a 22% slope but what possible numbers could the rise and run be which produce the 22% slope or what possible numbers would produce the 40%.
Real world math right here. Once students have come up with possible choices for the rise and run, pull out topographic maps for students to find the actual slope for each part of the trolley. Once students have these numbers, students can look at other trolleys , other cable cars both aerial and land based to see what type of slopes they have.
Final part of this is to choose a spot which requires a trolley or ski jump to get from one point to another. The location should have several possibilities for it so no one choice is right. Break students into several groups before providing the students with pictures, topographic map and ask them to provide a design for that location. They need to create a full presentation from a drawing of a the trolley or ski jump or cable car, to reasons why it was done that way. They are trying to sell the investors on selecting their group and their design for the project.
I love traveling because I see all sorts of interesting mathematical problems wherever I go. Let me know what you think, I'd love to hear. Have a great door.
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