% Script  le rocket2.m % Computes time to reach desired height. % Set the data values. h_desired = 40000; m_e = 100; q = 1; u = 8000; g = 32.2; dt = 0.1; b = 50; % Compute values at burnout, peak time, and height. m_0 = m_e + q*b; v_b = u*log(m_0/m_e) - g*b; h_b = ((u*m_e)/q)*log(m_e/(m_e+q*b))+u*b - 0.5*g*b^2; t_p = b + v_b/g; h_p = h_b + v_b^2/(2*g); % If h_p > h_desired, compute time to reached h_desired. if h_p > h_desired h = 0; k = 0; while h < h_desired % Compute h until h = h_desired. t = k*dt; k = k + 1; if t <= b % Burnout has not yet occurred. h = (u/q)*(m_0 - q*t)*log(m_0 - q*t)... + u*(log(m_0) + 1)*t - 0.5*g*t^2 ... - (m_0*u/q)*log(m_0); else % Burnout has occurred. h = h_b - 0.5*g*(t - b)^2 + v_b*(t - b); end end % Display the results. disp(‘The time to reach the desired height is:’) disp(t) else disp(‘Rocket cannot achieve the desired height.’) end