Question

EFC 3213 COMPUTING II (NUMERICAL METHOD) Assignment 2. Group Assignment (3-4 person per group) Students must use MATLAB software in order to solve the problems given and write a report containing all the necessary evidence proving that the work has been done. Any theory, assumption or any related discussion related in solving the problem must be inserted into the report. The MATLAB programming code should be attached as appendix to the report and shall not be put as the report itself. Good Luck! Problem 1. Curve Fitting. A theoretical mathematical model for the velocity of the parachutist was given as the following (1-) gm v(t) Where v velocity (m/s), g gravitational constant (9.8 m/s), m equal to 68.1 kg, and c drag coefficient of 12.5 kg/s. The model predicts the velocity of the parachutist as a function of time. mass of the parachutist Besides that, an altermative empirical model for the velocity of the parachutist is given by gm c 3.75+t Ifthe measured value for the velocity is given in the Table 1, by using MATLAB software, test and compare the adequacy of these two mathematical models. Which model is perfectly match with the measured value. (Plot all the related graph) Table 1 Measured velocities for the falling parachutist Time, s Measured v, m/s 10.00 16.30 23.00 4 27.50 5 31.00 6 35.60 7 39.00 41.50 42.90 10 45.00 11 46.00 12 45.50 13 46,00 14 49.00 15 50,00 Hint the adequacy of the models can be tested by plotting the model-calculated velocity versus. the measured velocity. The best model line have a slope of 1, an intercept of 0, and ar 1

Answer 1

%%% Matlab code %%%

clc;
close all;
clear all;
g=9.8;
m=68.1;
c=12.5;
t=1:15;
v_m=[10 16.3 23 27.5 31 35.6 39 41.5 42.9 45 46 45.5 46 49 50];
v1=g*m/c*(1-exp(-c/m*t));
v2=g*m/c*(t./(3.75+t));

mse1=sqrt(sum((v1-v_m).^2));

plot(t,v_m,'*')
hold on
plot(t,v1,'g');
hold on
plot(t,v2,'r');
legend('Measured value','Mathmatical model','Empirical model');
xlabel('Time t');
ylabel('Velocity v');
grid on
mse1=sqrt(sum((v1-v_m).^2));
mse2=sqrt(sum((v2-v_m).^2));
if (mse1 < mse2)
fprintf('Theoretical mathmetical model is better than empirical model');
else
fprintf('empirical model is better than Theoretical mathmetical model ');
end

OUTPUT:

Theoretical mathmetical model is better than empirical model

50 Measured value Mathmatical model 45 Empirical model 40 35 30 20 15 10 5 0 10 15 Time t Velocity v 25