The free body diagram of the rocket can be shown as,
According to free body diagram, the net force acting on the rocket is given as,
[tex]F=T-f-mg[/tex]According to Newton's law,
[tex]F=ma[/tex]Plug in the known value,
[tex]\begin{gathered} ma=T-f-mg \\ a=\frac{T-f-mg}{m} \end{gathered}[/tex]Substitute the known values,
[tex]\begin{gathered} a=\frac{1.5\times10^7\text{ N-}4.7\times10^6\text{ N-(4.75}\times10^5kg)(9.8m/s^2)(\frac{1\text{ N}}{1kgm/s^2})}{4.75\times10^5\text{ kg}} \\ =\frac{1.5\times10^7\text{ N-}0.47\times10^7\text{ N-}0.47\times10^7\text{ N}}{4.75\times10^5\text{ kg}} \\ =\frac{0.56\times10^7\text{ N}}{4.75\times10^5\text{ kg}}(\frac{1kgm/s^2}{1\text{ N}}) \\ \approx11.8m/s^2 \end{gathered}[/tex]Thus, the acceleration of the rocket is 11.8 m/s2.
