The function $\backslash ($ v$($t$)=-$g t$-$k L N$\backslash$left$(1-\backslash$frac$\{$r$\}\{$m$\}$ t$\backslash$right$)\backslash )$ models the velocity of a rocket shooting skyward in meters per second where $\backslash ($ t $\backslash )$ represents seconds since launch. What function models the rocket's height $($position relative to launch pad$)?$

For the curious, $\backslash ($ m $\backslash )$ represents initial mass of fuel in kilograms, $\backslash ($ r $\backslash )$ represents the rate of fuel burn in kilograms per second, $\backslash ($ k $\backslash )$ represents the velocity of the exhaust gases in meters per second, and $\backslash ($ g $\backslash )$ is the usual constant for acceleration due to gravity. In other words, $\backslash ($ m$,$ r$,$ k $\backslash ),$ and $\backslash ($ g $\backslash )$ are constants.