Download Introduction to Computational Methods - Assignment Set #8 | ESM 2074 and more Assignments Engineering in PDF only on Docsity! AOE/ESM 2074 Introduction to Computational Methods H.W. Set 8 due 1 November 2001 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 x axis. 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 bisection1.m code to implement this procedure. Test both your procedure and the built-in fzero.m procedure on finding a zero of 1− x exp(x) near x = 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 d and 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 a Matlab function to accept the measured time (input) and return the depth estimate. The speed of sound is about 340 m/s and the acceleration due to gravity is about 9.81 m/s2. Make a graph with measured time on the abscissa (x axis) and well-depth on the ordinate (y axis). 3. The level-flight drag of an aircraft can be approximated (in suitable non-dimensional units) by an expression of the form D W = 1 2(L/Dmax) ( V 2 + 1 V 2 ) Here D is the level-flight drag force and W is 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 = 10 and T/W = .3. 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. 1
