Given data:
* The mass of the roller coaster is m = 800 kg.
* The total mechanical energy is E = 392000 J.
* The kinetic energy at the particular height (let h') is K = 92000 J.
Solution:
The potential energy of the roller coaster at h' is,
[tex]\begin{gathered} U=E-K \\ U=392000-92000 \\ U=300000\text{ J} \end{gathered}[/tex]The potential energy in terms of height and mass is,
[tex]U=\text{mgh}[/tex]where g is the acceleration due to gravity,
Substituting the known values,
[tex]\begin{gathered} 300000=800\times9.8\times h \\ 300000=7840\times h \\ h=\frac{300000}{7840} \\ h=38.3\text{ m} \end{gathered}[/tex]Thus, the height of the roller coaster from the ground is 38.3 meters.
