When the rocket is in the air, it experiences gravitational force due to earth. Gravitational force is a conservative force. Therefore, applying conservation of mechanical energy

$$\begin{gathered} -\frac{GMm}{R}+\frac{1}{2}m{u}^2=-\frac{GMm}{\left(R+h\right)} \\ \Rightarrow -\frac{GM}{R}+\frac{1}{2}{u}^2=-\frac{GM}{\left(R+h\right)} \\ \Rightarrow -\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}}{6.4\times {10}^4}+\frac{{4000}^2}{2}=-\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}}{\left(6.4\times {10}^4+h\right)} \\ \Rightarrow h=914.28 \mathrm{km} \end{gathered}$$