Suppose that
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Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis
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- Suppose that a parachutist with linear drag (m=50 kg, c=12.5kg/s) jumps from an airplane flying at an altitude of a kilometer with a horizontal velocity of 220 m/s relative to the ground. a) Write a system of four differential equations for x,y,vx=dx/dt and vy=dy/dt. b) If theinitial horizontal position is defined as x=0, use Euler’s methods with t=0.4 s to compute the jumper’s position over the first 40 s. c) Develop plots of y versus t and y versus x. Use the plot to graphically estimate when and where the jumper would hit the ground if the chute failed to open.arrow_forwardUse the dsolve() function to solve the differential equation 8Dy3(t) = cos(20t) + sin(2t) for initial conditions y(10) = 50, Dy(0) = 0, Dy2(0) = 0, and y(10) = 5, Dy(0) = 0, Dy2(0) = 3. Plot your solutions on a single figure as a solid curve for the first set initial conditions and a dotted curve fo rthe second set of initial conditions for time t = -10 to 20. Make sureu to label both axes and title your figure, and turn on the plotting legend. Set teh y-axis limits to [-150 200].arrow_forwardDetermine the drag coefficient c needed for a parachutist of mass m=68.1kg to have a velocity of 40m/s after free-falling for time t=10s. Note: The acceleration due to gravity is 9.8m/s2. Use the Regula Falsi methodarrow_forward
- using matlab solve this physics problem The Green Monster is a wall 37 feet high in left field of Fenway Park in Boston. The wall is 310 feet from home plate down the left-field line. Assuming that the batter hits the ball 4 feet above the ground, and neglecting air resistance, determine the minimum speed the batter must give to the ball to hit it over the Green Monster. In addition, find the angle at which the ball must be hit at this minimum speed. Plot the trajectory of the ball off the bat; be sure to provide appropriate axis labels.arrow_forwardThe displacement of an oscillating spring can be described by x = A cos(wt) where x = displacement at time t, A = maximum displacement, w = angular frequency, which depends on the spring constant and the mass attached to the spring, and t = time. Find the displacement, x, with maximum displacement A of 4 cm, for times from 0 to 120 seconds with increments of 30 seconds, and angular frequencies from 0.4 to 0.6 radians/sec, with increments of 0.1 radians/sec. The displacement for all combinations of times and angular frequencies needs to be calculated. Use meshgrid. Display your results in a matrix with angular frequencies along the top row and times along the left column like so (you may put zero, 0, or NaN, in the upper left corner:arrow_forwardA researcher would want a system he can use for his research work. The system should ask for a minimum value, maximum value and interval mode. Such values will be used as the minimum and maximum values of x to solve the given equation: f(x) = x3 – 4x2 + 10x - 4arrow_forward
- In a place called BW is well known for its weather. The weather condition is not extreme at all and many people want to migrate there only for the characteristic of the place. it rains on one fourth of the days. The local evening newspaper attempts to predict whether or not it will rain the following day. Three quarters of rainy days and four fifths of dry days are correctly predicted by the previous evenings paper. Given that this evenings paper predicts rain, what is the probability that it will actually rain tomorrow?arrow_forward2. Heat conduction in a square plate Three sides of a rectangular plate (@ = 5 m, b = 4 m) are kept at a temperature of 0 C and one side is kept at a temperature C, as shown in the figure. Determine and plot the ; temperature distribution T(x, y) in the plate. The temperature distribution, T(x, y) in the plate can be determined by solving the two-dimensional heat equation. For the given boundary conditions T(x, y) can be expressed analytically by a Fourier series (Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley and Sons, 1993):arrow_forwardDetermine P(A x B) – (A x B) where A = {a} and B = {1, 2}.arrow_forward
- Consider nonnegative integer solutions of the equation x1+x2+x3+x4+x5+x6=30. How many different solutions are there? How many solutions also satisfy: for every i∈{1,2,3,4,5,6}, xi is positive and even?arrow_forwardEstimate the integral of f(x)=sin(x)/x between 0 and 1 using Simpson's 3/8 rule. Use n=12arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole