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 $v_e$ (relative to the rocket). A model for the velocity of the rocket at time $t$ is given by the equation $$v(t)=-gt-v_e\ln\left(\frac{m-rt}{m}\right)$$ where $g$ is the acceleration due to gravity and $t$ is not too large. If $g=9.8\,m/s^2,$ $m=15000\,kg,$ $r=160\,kg/s,$ and $v_e=3000\,m/s,$ find the height (in meters) of the rocket one minute after liftoff.

Height = meters