The analytic approach to determine the optimal conditions for maximizing altitude of a sounding rocket is extended to the case in which the rocket flies in a standard atmosphere where the air density as well as the gravitational acceleration changes with altitude. The one-dimensional rocket momentum equation including thrust, gravitational force, and aerodynamic drag is solved. Flight in the standard atmosphere is analyzed by dividing the whole flight time into small intervals where the drag parameter and gravitational acceleration can be treated as constant in each interval. The analytic approach gives piecewise exact solutions of the rocket velocity and altitude that agree well with the numerical ones. A characteristic equation exists and provides accurate predictions of the optimal conditions for maximizing altitude at burn-out state or apogee.