Water going down a waterfall, where is it warmer?

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The discussion revolves around calculating the temperature difference of water at the top and bottom of a 120m waterfall, using the specific heat capacity of water. It highlights the conservation of energy principle, where potential energy converts to kinetic energy and then to thermal energy. The user seeks guidance on how to relate these energy forms to determine the temperature increase of the water. They reference the equation E = (m)(c)(T) to connect heat energy with temperature change. The conversation emphasizes the need for a calculation method to quantify the temperature difference resulting from the fall.
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Homework Statement


Consider a waterfall that is 120m high. How much warmer is the water at the bottom of the waterfall than at the top? The specific heat capacity of water is 4186J/ kg*°C.


Homework Equations


Conservation of Energy


The Attempt at a Solution



Eg [top] = Ek [just before the water hits the ground]
(m)(g)(h) = 1/2(m)(v)^2


I don't know how to compare the warmness of the top to the bottom, or how to get it calculation-wise. Does this have to do with:

E = (m)(c)(T)?
Where "E" is the heat energy?
 
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It's a straightforward conservation of energy.

(1) Potential energy before the fall > (2) Kinetic energy just before it hits > (3) Thermal energy in the water.

You can go straight from (1) to (3)
 
But would you mind giving me a hint as to how I would go about with the calculations?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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