## Peeking At Cedar Point

Back a couple months I wrote way too much about the problem of how many rides to expect on Cedar Point’s Disaster Transport, if we chose whether to re-ride it based on a random event. It struck me there’s another problem created by the amusement park’s removal of the indoor bobsled roller coaster. This one is based on Transport Refreshments, the block of food and drink stands which stood by the removed Disaster Transport and Space Spiral.

Specifically: what’s to become of that area? When my Dearly Beloved and I visited in late September the area was walled off, for construction, but one could rationalize any kind of fate for it. The block might get torn down to provide space for new rides; it might be left as-is, with the name Transport Refreshments left as a mysterious reference that new visitors would have to learn something of park history to understand; or the stands might be re-themed to the GateKeeper roller coaster being built. By now, probably, park-watchers really know, but when we visited, there wasn’t any telling, except by peeking over the fence.

The problem is you can’t see very much, because the fence is in the way. I’m tall and can hold my camera pretty high and so could get glimpses showing that the buildings hadn’t as of late September been torn down, and that they even had the sign in place, but that doesn’t mean much.

It does suggest a cute problem, though, one that’s easy to solve using calculus and maybe is solvable by easier tools. That problem’s, how do you get the best view of the hidden Transport Refreshments? Going up close to the fence means the fence obscures more of your field of view; getting farther away — the ground is roughly level here — reduces the field of view obscured by the fence, but also reduces the Transport Refreshments’ angular diameter. There’s probably a best spot to see what’s beyond, but, where is it?

To turn this into a word problem, let’s pretend things are nice round numbers: that the person doing the viewing has eyes about six feet off the ground, that the fence is eight feet tall, and that — four feet past the fence — the main sign for the Transport Refreshments stands twelve feet tall. I am sure these arbitrarily plucked numbers will produce only good results.

### 2 Responses to “Peeking At Cedar Point”

1. There is an elegant non-calculus solution to this one. The details take a little bit of work, but here’s the outline…

Draw a diagram with A = top of the sign, C = top of the fence, and a line L showing all possible eye-level positions. Our object is to pick a point B on L that maximises angle ABC.

Abj qenj n pvepyr B guebhtu N naq P gung whfg gbhpurf Y. (Gurer ner npghnyyl gjb fhpu pvepyrf; cvpx gur bar gung gbhpurf vg bhgfvqr gur srapr.) Znex O ng gur cbvag jurer guvf pvepyr gbhpurf Y.

Gb frr gung guvf vf gur bcgvzny cbfvgvba: pbafvqre nal bgure yrtny cbvag O’ ba Y. Qenj gur pvepyr B’ gung cnffrf guebhtu N, P, naq O’. Lbh fubhyq or noyr gb fngvfsl lbhefrys gung B’ zhfg unir n ynetre enqvhf guna B.

Ol whqvpvbhf hfr bs gur “natyrf fhograqrq ol fnzr nep” gurberz, lbh pna gura crefhnqr lbhefrys gung gur natyr NOP vf ynetre guna NO’P. Urapr O vf gur bcgvzny fbyhgvba.

Sebz gurer, vg orpbzrf n fvzcyr cvrpr bs Pnegrfvna trbzrgel jvgu fbzr fvzhygnarbhf rdhngvbaf gb fbyir. Vs V’ir tbg vg evtug, juvpu vf rkgerzryl hayvxryl, gur nafjre vf (gjb cyhf fdhner ebbg bs gjragl-sbhe) srrg.

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