What is the speed as it hits the wheel?

[engineer2010]

Homework Statement

Water falls onto a water wheell from a height of 2.0m at a rate of 95kg/s (a) If this water wheel is set up to provide electricity output, what is the max power output. (b) What is the speed as it hits the wheel?

Homework Equations

Ep= mgh Ek= 1/2mv^2

The Attempt at a Solution

I know that the water initally has both potential and kinetic energy as it falls but i am unsure as to how i use the rate in these equations and also which power equation(s) I use once i get to that stage.

 

[Astronuc]

Well the elevation of a mass m in a gravitational field provides for gravitational potential energy (GPE) by virtue of mgh, where h is the elevation above some reference point.

If an object at h is released and it falls through distance h, then GPE decreases by mgh and that GPE is transformed to kinetic energy 1/2 mv², and neglecting air resistance mgh = 1/2 mv².

If one has a mass flow rate \dot{m}, then the rate at which energy (described above) is delivered is simply \dot{m}gh, and the rate of energy delivery/transformation is power.