A rocket accelerates by burning its on-board fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is , the fuel is consumed at rate , and the exhaust gases are ejected with constant velocity (relative to the rocket). A model for the velocity of the rocket at time is given by the equation
where is the acceleration due to gravity and is not too large. If and find the height (in meters) of the rocket one minute after liftoff.