A simple formula to estimate the upward velocity of a rocket (neglecting the aerodynamic drag) is:
v(t)=u\ln (\frac{m_0{}}{m_0{}-qt})-gt
where t = time, v = upward velocity, u = the velocity at which fuel is expelled relative to the rocket, m0 = the initial mass of the rocket at time t = 0, q = the fuel consumption rate, and g = the downward acceleration of gravity.
Develop a MATLAB function which, for given parameters u, m0, q, and g, and a specified velocity v*, computes the time t* that the rocket reaches this velocity.
Hint:
(1) Formulate this problem into a root-finding problem, and solve it using the MATLAB built-in function "fzero".
(2) The initial bracketing interval (or initial guess) for "fzero" must be within the domain of the root-finding function. Note that the above function v(t) has a bounded domain (due to "ln").
The function should start off like the one below:
function tstar = fzero_rocket_example(u, g, q, m0, vstar)
%% Input
% m0: initial mass of rocket at time t=0
% g: gravitational constant
% q: fuel consumption rate
% u: velocity at which fuel expelled relative to rocket
% vstar: upward velocity value for which tstar is to be determined
%
%% Output
% tstar: the time that the rocket reaches the specified velocity, vstar. (scalar)
%% Write your code here.
tstar = 0;
end
