Kerepakupai vena in venezuela, more commonly known as angel falls, is the world's highest waterfall with a height of 979 m and 47 different plunges. the longest plunge (for the water) is 807 m. at the bottom of the fall, the kinetic energy of the water is converted into thermal energy. this results in a temperature increase of the water. if the water has a temperature of 17.1°c when it gets to the bottom of the plunge, what was the temperature at the top of the plunge? the specific heat of water is 1.00 kcal/(kg · °c).

Explanation:

We will use the the conservation of energy principle to solve this problem. In this sense, for the case of the Kerepakupai Vena waterfall the energy at the top must be equal to the energy at the bottom:

(1)

(2)

(3)

Where and are the kinetic an potential energy at the top of the waterfall, respectively; and and are the kinetic an potential energy at the bottom of the waterfall, respectively.

Since we are told the kinetic energy of the water is converted into thermal energy , we have:

and

Hence (2) and (3) are rewritten as:

(4)

(5)

Then:

(6)

On the other hand we know the potential energy for both cases is:

and

Where:

is the mass of water

is the acceleration due gravity

is the height at the top

is the height at the bottom of the waterfall

In addition, the thermal energy for both cases is:

 and

Where:

 is the specific of water

 is the temperature at the top

 is the temperature at the bottom

So, keeping this in mind, equation (6) is rewritten as:

(7)

Since :

(8)

Finding :

(9)

Solving:

(10)

(11)

Now that we have and we can finally find :

(12)

(13)

Therefore:

frequency or wavelenth of em radiation in a vacuum