Question

MATLAB WORK PLEASE

The upward velocity of a rocket can be computed from the following formula: v=u* In mo -91 mo-91 where v = upward velocity, u = the velocity at which fuel is expelled relative to the rocket, me = the initial mass of the rocket at time t=0,9 = the fuel consumption rate, and g = the acceleration due to gravity. Compute the time tro at which v reaches an arbitrary value using the bisection method. Use the following parameters: me = 1603; % Initial rocket mass [kg] (scalar) = 9.81; % Gravitational constant [m/s^2] (scalar) = 2600; % Fuel consumption rate [kg/s] (scalar) u = 1800; % Velocity at which fuel is expelled relative to rocket [m/s] (scalar) tl = 10; % Initial guess for the lower root [s] (scalar) tu = 40; % Initial guess for the upper root [s] (scalar) Use a stopping criterion of e, = 0.0001. In other words, stop the search when f (troot) Ses. Function C Reset D MATLAB Documentation u: i function t_root = Rocketvelocity(me,8,9,u,v,ti, tu, es) 2 % Inputs: 3 % me: Initial mass of rocket at time t= [kg] (scalar) 4 % 8 Gravitational constant [m/s^2] (scalar) 5 % 9: Fuel consumption rate [kg/s] (scalar) 6 % Velocity at which fuel is expelled relative to rocket [m/s] (scalar) 7 % Rocket upward velocity [m/s] (scalar) 8 % tl: Initial guess for the lower root [s] (scalar) 9 % tu: Initial guess for the upper root [s] (scalar) 10 % es: Stopping criterion [ND] (scalar) 11 % 12 % Output: 13 % t_root: Time when the rocket reaches the specified velocity [s] (scalar) 14 % 15 % Write your code below:

Answer 1

clc
clear

m0 = 160e3;
g = 9.81;
q = 2600;
u = 1800;
tl = 10;
tu = 40;
es = 0.0001;
v = 900;        % Arbitary velocity taken by choice
t_root = RocketVelocity(m0,g,q,u,v,tl,tu,es);

function t_root = RocketVelocity(m0,g,q,u,v,tl,tu,es)
    syms t
    f = @(t) v-(u*log(m0/(m0-q*t))-g*t);
    a = tl;
    b = tu;
    error = 1;
    while (error > es)
        t_root = (a+b)/2;
        if (f(a)*f(t_root) < 0)
            b = t_root;
        else
            a = t_root;
        end
        error = abs(f(t_root));
    end
    fprintf('Root is %f \t and the error is %f \n',t_root,error)
end

Root is 29.810624    and the error is 0.000038