Question

1.) Euler Method (estimated time 11min) For the second-order drag model (see Eq. (1)), compute the velocity of a free-falling parachutist using Euler's method for the case where m 80 kg and cd- 0.25 kg/m. Perform the calculation from t 0 to 0.3 s with a step size of 0.1 s. Use an initial condition that the parachutist has an upward velocity of 20 m/s at t 0. Att- 10 s, assume that the chute is instantaneously deployed so that the drag coefficient jumps to 1.5 kg/m. dv dt Hint: upward velocity of 20 m/s implies that vo -20m/s t [sec] 0 0.1 0.2 0.3 v [m/sec] -20 19.1440 18.2775 17.4009 dv/dt 8.5600 8.6647 8.7660 8.8638 dv 0.8560 0.8665 0.8766 0.8864

PLEASE HELP! I need to write a MATLAB code for this Euler approximation for finding the velocity of a parachutist at given time iterations. The answers are provided so you can check to see if the code works. I need to see it done in actual MATLAB program so I can understand the coding methodology better.

Answer 1

Hey,

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clear all
clc
Cd=0.25;
t=0:0.1:0.3;
v=[];
v(1)=-20;
m=80;
g=9.81;
f=@(t,V) g-Cd*(V^2)/m;
fprintf('For t=%.1f, v=%.4f, dv/dt=%.4f and dv=%.4f ',t(1),v(1),f(t(1),v(1)),f(t(1),v(1))*0.1);
for i=1:length(t)-1
v(i+1)=v(i)+0.1*f(t(i),v(i));
dvdt=f(t(i+1),v(i+1));
dv=0.1*dvdt;
fprintf('For t=%.1f, v=%.4f, dv/dt=%.4f and dv=%.4f ',t(i+1),v(i+1),dvdt,dv);
end

99.81 fprintf ( . For for i-l:length (t)-1 10 - t=% . If, v-% . 4f, dv/dt=%·4f and dyst. 4f\n' , t (1), ν (1), f (t (1), ν (1) ) , f (t (1), ν (1) )"0. Ip ; 12 dvdt-f (t (1+1),v(i+1)) 15 16 - Command Window end ④ New to MATLAB? Watch this Video see Examples, or read GettingStarted. dv=0 .8560 dv=0 . 8665 dv-0.8766 dv=0 . 8864 For For For For S> t=0 . 0, t=0.1, t-0.2, t=0. 3, v=-20.0000, v=-19.1440, v--18.2775, v=-17, 4009, dv/dt=8.5600 dv/dt=8.6647 dv/dt-8.7660 dv/dt=8. 8638 and and and and

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