A rocket accelerates by burning its onboard 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 r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). A model for the velocity of the rocket at time is given by the equation where g is the acceleration due to gravity and is not too large.

If g = 9.8, m/s2, m = 30,000 kg, r =160 kg/s, and ve = 3000m/s, find the height of the rocket one minute after liftoff.

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m - rt - -gt - v, In- v(1) ह