This question involves the concepts of the law of conservation of energy, kinetic energy, and potential energy.
The height of the hill is "166.76 m".
According to the law of conservation of energy at the highest point of the roller coaster ride, that is, the hill, the whole (maximum) kinetic energy of the roller coaster is converted into its potential energy:
[tex]Maximum\ Kinetic\ Energy\ Lost = Maximum\ Potential\ Energy\ Gain\\\\ \frac{1}{2}mv_{max}^2=mgh\\\\ h=\frac{v_{max}^2}{2g}[/tex]
where,
Therefore,
[tex]h=\frac{(57.2\ m/s)^2}{2(9.81\ m/s^2)}\\\\ [/tex]
h = 166.76 m
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