Platform diving: How deep does one go into the water? I am a platform diver. I am trying to figure out how deep in the water I go depending on which platform I dive from.
The platforms are 1m, 3m, 5m, 7.5m and 10m above the water surface.
By ignoring air resistance (we assume that I do not do any tricks) I can easily compute the energy that my 90 kg body has when it is hitting the water:
E = mgh = 0.5mv^2

My problem is to find the deceleration in water and thus how deep my feet will go into the water before coming to a halt. We can assume that I stand straight and fall straight down and have a height of 190cm.
How do I compute that?
 A: There are bound to be more detailed answers and analysis, but let's look at one of the oldest possible results in the field. Isaac Newton proposed that, for bodies of equal density, the penetration depth during ballistic impact is equal to the length of the penetrating body. Note -- this is independent of the speed (which means independent of the height) of the diver. 
Regular water has a density of $1000 kg/m^3$ and the human body is slightly less dense at $985 kg/m^3$. If we assume that this is approximately valid still and we assume the diver is 6 feet tall and extends his or her arms above her head during the dive (and that arms are, roughly, 3 feet long) giving the diver a body length of 9 feet, the penetration depth would be:
$$ d = 9 * 985/1000 $$
which gives an answer of 8.89 feet. 
Now, the part that might be confusing -- this is true regardless of the height from which the diver dove. This is counter-intuitive, but ultimately it means that a lower-height dive causes less acceleration upon entry into the water than a higher dive does. So a diver from 1 meter would experience far less g-forces upon entry compared to a 10 meter diver, but they would both go down to approximately the same depth. 
