Question

Kingda Ka has a maximum speed of 57.2 m/s. Determine the height of the hill on this roller coaster. Explain to get full credit, show work!

Answer 1

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".

LAW OF CONSERVATION OF ENERGY:

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:

$Maximum\ Kinetic\ Energy\ Lost = Maximum\ Potential\ Energy\ Gain\\\\ \frac{1}{2}mv_{max}^2=mgh\\\\ h=\frac{v_{max}^2}{2g}$

where,

• h = height of the hill = ?

• $v_{max}$ = maximum velocity = 57.2 m/s

• g = acceleration due to gravity = 9.81 m/s²

Therefore,

$h=\frac{(57.2\ m/s)^2}{2(9.81\ m/s^2)}$

h = 166.76 m

Learn more about the law of conservation of energy here:

brainly.com/question/101125