The Outer Banks is a sand bar extending for hundreds of miles along the east
coast of the United States, mostly along the coast of North Carolina. The sand
bar is broken by shallow channels that connect the Atlantic Ocean on the east
to the shallow salt water sounds on the west. The result is a chain of long,
thin islands only a few feet above sea level.
The Outer Banks were the site of Sir Walter Raleigh's lost colony and the
Wright Brothers' first powered flight. It is also known for surf fishing,
hazardous navigation, and impressive riptides.
The Wright Brothers' first powered flight was made from the highest natural
point along the Outer Banks at Kitty Hawk. Kitty Hawk is a broad sand dune
that peaks at 38 feet above sea level. The essence of this problem is to
determine how far out in Albemarle Sound one can see from the summit of Kitty
Hawk.
For a figure of the problem please refer to the main menue of the tutor.
You are sitting on the top of Kitty Hawk on a calm day with no waves. You are
watching a friend swimming across the sound toward the mainland. Because of
the curvature of the earth, your friend will eventually disappear across the
horizon. How far away (in feet) can your friend get before he disappears from
view? We're interested in finding the maximum possible straight line distance
from your eye to your friend.
See the figure for a sketch of what computations are required to solve this
problem. Notice that the solution involves using the Pythagorean Theorem to
solve for the unknown side of a triangle. The sketch is not to scale, so be
careful to notice that the unknown side is extremely small compared to the two
known sides, which are almost identical in length.
Now you should experiment with calculating the straight line distance using
floating point computations. Begin by setting the floating point precision to
6digits. Compute the value of the formula that you derived. Be sure that
all of the numbers that you include in the formula are floating point
constants---not integers. (The correct answer is approximately 39,857 feet.)
Repeat this process using successively fewer digits of accuracy. Is what
happens what you expected? Can you explain what's going on? Think about these
questions before continuing.
Prepare a table showing the distance that you calculate for each level
of precision.