When trying to come up with a model for a problem, it is usually helpful to
draw a diagram. Doing so will often lead directly to a model, since the act of
drawing a diagram forces you to simplify and idealize the problem. Study our
diagram of the Kitty Hawk problem
carefully. See if you can identify any ways in which we have idealized the
actual problem.
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What we have just done amounts to assessing the modeling phase prior to
considering the method and implementation. It is a good idea to assess a model
before proceeding, as this will sometimes keep you from wasting time on a model
that you later decide is seriously flawed. The assumptions that we just listed
seem reasonable for the moment. We'll return to them after we've solved the
problem and see if we can quantify their effects on the eventual answer.
Besides leading us to a workable model, the diagram reveals an ambiguity in the
problem statement. Can you see what that ambiguity is?
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We will (rather arbitrarily) decide that we are interested in the line-of-sight
distance from the summit of Kitty Hawk to your friend in the sound. We will do
this because it leads to a simple model of the problem that can be solved using
a familiar method. What are the model and the method?
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All we need to know to proceed is the height of Kitty Hawk and the radius of
the earth. We have been told that the height of Kitty Hawk is 38 feet; let's
assume that the height is good to two significant digits. Let's assume that
the radius of the earth is 20,900,000 feet, significant to three digits.
Joseph L. Zachary
Hamlet Project
Department of Computer Science
University of Utah