Euler's Method

I'm trying to solve the following problem by the Euler Method:

A parachutist of mass 68.1 kg jumps out of a stationary hot air balloon. Use Eq. (1.10) to compute velocity prior to opening the chute. The drag coefficient is equal to 12.5 kg/s.

The book gives me already the equation which is:

v=53.44(1-e^-0.18355*t)

I understand that mi initial values are:

x(0)=0

y(0)=0

h=2

x(f)=12

where x is t and y is v.

The table below are the answers but my code doesn't give me that solution.

The answers i get by my code:

MY CODE

clear all
clc
f=@(x,y) 53.44*(1-exp(-0.1835*x)); %Write your f(x,y) function, where dy/dx=f(x,y), x(x0)=y0.
x0=input('\n Enter initial value of x i.e. x0: '); %example x0=0
y0=input('\n Enter initial value of y i.e. y0: '); %example y0=0.5
xn=input('\n Enter the final value of x: ');% where we need to find the value of y 
                                            %example x=2
h=input('\n Enter the step length h: '); %example h=0.2
 %Formula: y1=y0+h*fun(x0,y0);
 fprintf('\n x        y ');
while x0<=xn
    fprintf('\n%4.3f  %4.3f ',x0,y0); %values of x and y
    y1=y0+h*f(x0,y0);
    x1=x0+h;
    x0=x1;
    y0=y1;  
end

Answer 1

[Alan Stevens]

Since you are given velocity as a function of time, why don't you simply plug the desired values of time directly into the function?

vel = @(t) 53.44*(1 - exp(-0.18355*t));
t = [0; 2; 4; 6; 8; 10; 12; inf];
v = vel(t);
disp([t v])

Your function is a velocity, not a rate of change of velocity with time, so your statement

y1=y0+h*f(x0,y0);

doesn't result in a velocity, but a distance (though your timestep is probably too big for an accurate result).

[Alexa Fernanda Cantú García]

So how will the code would look like? Sorry, I have 3 weeks learning Matlab :)

[Alan Stevens]

The code I wrote above will calculate and display velocities (v) at the listed times (t).

[Alexa Fernanda Cantú García]

But then I wouldn’t be using Euler’s Method?...

[Alan Stevens]

To use Euler's method to calcuate veocities here, you need an acceleration (which you can get by differentiating the velocity function with respect to time). So, then your integration routine would look something like:

t = 0; 
v = 0;
while t <= tfinal
      v = v + h*acc(t);
      t = t + h;
end

where acc is your acceleration function and h is your timestep size (I'd suggest using a much smaller value than 2 to get reasonably accurate resuts).