Answer:
Approximately [tex]31\%[/tex] assuming that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex].
Explanation:
Consider an object of mass [tex]m[/tex] in a uniform gravitational field of strength [tex]g[/tex]. If the height of that object increased by [tex]\Delta h[/tex], the gravitational potential energy of that object would increase by [tex]m\, g\, \Delta h[/tex].
In this question, the mass of the rocket is given to be [tex]m = 0.55\; {\rm kg}[/tex]. Assume that [tex]g = 9.81\; {\rm N \cdot kg^{-1}}[/tex]. The rocket has gained a height of [tex]\Delta h = 23\; {\rm m}[/tex]. Thus, the gravitational potential energy of this rocket would have increased by:
[tex]\begin{aligned} m\, g\, \Delta h &= 0.55\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times 23\; {\rm m} \\ &\approx 124.1\; {\rm J} \end{aligned}[/tex].
In other words, the useful energy output from the combustion of the rocket fuel was approximately [tex]124.1\; {\rm J}[/tex].
The energy input to this rocket was given to be [tex]400.0\; {\rm J}[/tex]. Thus, the efficiency of the energy conversion would be:
[tex]\begin{aligned} \text{efficiency} &= \frac{(\text{useful energy out}\text{put})}{(\text{energy in}\text{put})} \times 100\% \\ &\approx \frac{124.1\; {\rm J}}{400.0\; {\rm J}} \times 100\% \\ &\approx 31\%\end{aligned}[/tex].
