Problem $3$: Consider a single$-$stage$-$to$-$orbit $($SSTO$)$ launch vehicle. Suppose the ideal velocity increment to achieve lowEarth orbit $($LEO$)$ is $v_{\text{i}\text{d}\text{e}\text{a}\text{l}}=9,100\frac{m}{s}($this ideal increment factors in gravity and drag losses and the small velocity boost from Earth rotation effects$).$ If a SSTO vehicle could achieve a structural coefficient of $0\mathrm{.}08$ and a specific impulse of $375$ s $,$ determine the vehicle's total liftoff massm$0$ required to deliver a payload mass of $1,000kg$ to LEO.