Respuesta :
Given data:
* The height of the initial hill is 9 m.
* The height of the final hill is 27 m.
Solution:
The amount of potential energy acquired by the roller coaster by reaching top of 27 m hill from the 9 m hill is,
[tex]U=mg(h_f-h_i)[/tex]where m is the mass of the roller coaster, g is the acceleration due to gravity, h_f is the final height of hill, and h_i is the initial height of the hill,
Substituting the known values,
[tex]\begin{gathered} U=m\times9.8\times(27-9) \\ U=m\times9.8\times18 \\ U=m\times176.4 \end{gathered}[/tex]The kinetic energy of the roller coaster at the start of motion from 9 m hill is,
[tex]K=\frac{1}{2}mv^2[/tex]where v is the velocity of the roller coaster at the start of the motion,
According to the law of conservation of energy,
[tex]\begin{gathered} K=U \\ \frac{1}{2}mv^2=176.4\times m \\ v^2=2\times176.4 \\ v^2=352.8 \\ v=18.78\text{ m/s} \end{gathered}[/tex]Thus, the minimum value of the velocity required to move the roller coaster to the top of 27 m hill from the 9 m hill is 18.78 m/s.
