Let us assume that rocket only runs in initial energy and not using its own to flying.
Also , let upward direction is +ve and downward direction is -ve .
Initial velocity , u = 58.8 m/s .
Acceleration due to gravity , [tex]g=-9.8\ m/s^2[/tex] .
Final velocity , v - = 0 m/s .
We know , by equation of motion .
[tex]v^2-u^2=2gh\\\\2gh_{max}=0^2-58.8^2\\\\h_{max}=\dfrac{0^2-58.8^2}{-2\times 9.8}\\\\h_{max}= 176.4\ m[/tex]
Hence, this is the required solution .
