Homework Assignment

These problems involve extensions and modifications to the Kitty Hawk problem described in this lesson.

1. What will affect the solution to the problem more: an error of one foot in measuring the height of the hill, or an error of 100 miles in measuring the radius of the earth?
2. In an attempt to make the solution to the Kitty Hawk problem even simpler, one student replaces the formula

   

   with

   

   Does this reduce the number of significant digits in the ultimate answer? Why or why not?

3. Assuming that the height of the hill is known to two significant digits and the radius of the earth to three, what are the upper and lower bounds on the distance out into the sound that the observer can see?
4. Suppose that a ship with a mast whose height is 53.5 feet is sailing on the sound, and that this measurement is accurate to three significant digits. How far from Kitty Hawk will the top of the mast be visible?