Hydroelectric power plants convert the gravitational potential energy of falling water into electrical power, typically by allowing the water to flow through a pipe called a penstock to rotate a generator located below it. Let the bottom of the penstock be the origin of a Cartesian coordinate system and the point at which the gravitational potential energy is zero.
a) Consider a penstock that is vertical and has a height of h = 61 m. How long, t in seconds, does it take water to fall from the top of the penstock to the bottom? Assume the water starts at rest.