AOE/ESM 2074
Introduction to Computational Methods
due 26 October 2000
1. The method of false positions (or regula falsi) is another way of implementing a root-
finging procedure along the lines of the bisection procedure described in class. Here
again, we have two points (the ends of an interval); at one point the value of the
user-specified function is positive, while at the other point it is negative. We draw a
straight line connecting the points on the graph and compute where the straight line
crosses the xaxis. The function is evaluated at the new point and depending on the
sign of the resulting value we replace one of the original points (the one with the same
sign for the function value).
Modify the bisection.m code so that the interval reduction procedure is done by this
new method. Test both your procedure and the bisection.m procedure on finding a
zero of 1 −xexp(x)nearx=2.
2. You want to estimate the depth of a well. To do this you drop a stone in the well
and wait to here the splash. Assume you release the rock from rest at ground level.
Work out an expression for the time it takes for the rock to fall to a depth dand for
the time it takes the sound to propagate from the bottom of the well back to your ear
(at ground level). Your experiment will provide a measurement of the sum of these
two times. Write Matlab function to accept the measured time and return the depth
estimate.
3. The level-flight drag of an aircraft can be approximated (in suitable non-dimensional
units) by an expression of the form
DOW =1
2L/Dmax V2+1
V2
Here DOW is the ratio of the level-flight drag force and the weight.
To maintain level-flight the engine must produce this amount of thrust (thrust equals
drag). Suppose we have an aircraft with L/Dmax =12andT/W =.4. Find the highest
possible level flight speed.
You should begin by drawing a graph of (normalized) drag as a function of the level
flight speed V. Your answer should include the graph, a listing of your code, and the
computed speed.
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