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 m, 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 timet is given by the equation v(t) = -gt – Ve т — rt In m where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s², m = 25000 kg, 160 kg/s, and Ve r = :3000 mls, find the height (in meters) of the rocket one minute after liftoff. %3D Height = meters

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