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 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 time t is given by the equation

v$($t$)=$gt $$ ve ln$$

m $$ rtm

where g is the acceleration due to gravity and t is not too large. If g $=9\mathrm{.}8$ m$/$s$2,$ m $=28,000$ kg$,$ r $=130$ kg$/$s$,$ and ve $=2,800$ m$/$s$,$ find the height of the rocket one minute after liftoff. $($Round your answer to the nearest whole meter.$)$