Clyde, a barnstormer, wants to perform his daredevil stunts and aerobatics but flight controllers understandably don't want him endangering aviation in the vicinity of Cherry Capital Airport. Therefore, they have directed him to take off from Cherry Capital (N 44 44.656, W 085 34.433) and to ascend at a constant angle and heading until he reaches an altitude of 2400 meters at a location northeast of Traverse City. At that point (which happens to be directly over the Barnstormers geocache!) he is free to begin his antics. As Clyde ascends enroute his performance, he notices that he reaches an altitude of 800 meters exactly over location N 44 46.104, W 085 32.178. Clyde's general route is shown below.
The geocache is located at the point exactly 2400 meters below where Clyde is permitted to begin his performance.
As illustrated above, this puzzle can be solved using principles of similar triangles. For the purposes of this exercise consider the earth flat.
Barnstormers were the extreme sports practitioners of their day (mainly in the 1920's) and performed all sorts of amazing aerobatics and stunts (such as wing walking and transfers between planes in flight). Clyde Pangborn (pictured at left) was one of the most famous of the breed. Later in his career he made the first nonstop trans-Pacific flight from Japan to the United States.
The area in which the geocache is hidden is a beautiful, probably lesser known, nature area. As befits a cache dedicated to flight, at the time the cache was placed there were an eagles nest and two roosting bald eagles in the distance at bearing 170 degrees from the cache location. Finders of the cache are to trade aviation related items, but as always, any geotrade items are welcome.
The coordinates at the top of this page are not for the cache, but are for a nearby place in which to park and access the area. If you have trouble figuring this one out, feel free to contact Whitard for some help.
Have fun with his geometry/mathematics problem and this beautiful nature area!