Explaining depths reached by swimmer by conservation of energy/momentum

[Jazz]

Homework Statement

If you dive into water, you reach greater depths than if you do a belly flop. Explain this difference in depth using the concept of conservation of energy. Explain this difference in depth using what you have learned in this chapter**.

** It is referring to the chapter of Conservation of Momentum.

Homework Equations

$\Delta KE + \Delta PE + \Delta OE + W_{nc} = constant$

$\Delta p_1 + \Delta p_2 = constant$

The Attempt at a Solution

I'm not sure how to explain the difference just by conservation of energy and/or momentum.

If I assume that in both cases (diving and doing a belly flop) the center of mass of the person falls the same height $h$ before reaching the surface of the water, then the velocity will be $v$, and hence there will be no difference between KE's and between momenta.

My attempt: It seems clear to me that, when diving, the KE is removed through a longer distance than in the other situation, which has to do with the area facing the fluid. A greater area facing the fluid (the belly flop case) implies a greater mass of water ''gathered'' underneath and hence a greater upward force against the person's motion. Consequently, it will remove their momentum in a shorter amount time.

When diving, the ''head-on collision'' is against a smaller area (less water molecules underneath), supplying a smaller upward force that will have to act for a longer amount of time to finally bring the person to rest (having imparted their momentum to the surrounding water molecules in the process).

In both cases the force is a nonconservative one, doing work against the person’s motion, removing KE from it while being transferred to other forms (since it increases the random motion of water molecules, would it be heat?).
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I think it's too vague. I'm not satisfied by having brought water molecules into the picture. If I use the equations as guidance, there is no variable I can plug in specifying whether the person falls with the stomach of with their feet first (I feel that I'm confined to give a poor explanation).

I guess that using some concepts of fluids (density, buoyancy and pressure) I would be able to provide a better explanation. It seems that I tried to explain it by the difference in pressure, but I think I shouldn’t try that path yet, since I will learn that in later chapters.

Is there another way I can think about it?

Thanks !

 

[NascentOxygen]

Hmmm. I would have just said something along the line of streamlined shape, less water pushed aside, lower fluid resistance, hence lower energy losses per metre travelled? Is that not enough?

 

[Jazz]

I think it's good :)

I'm afraid I've spent more time than necessary thinking about this ]: