newtonian mechanics - Jumping into water

Two questions:

1. 
   

   Assuming you dive head first or fall straight with your legs first, what is the maximal height you can jump into water from and not get hurt?
   In other words, an H meter fall into water is equivalent to how many meters concrete-pavement fall, force wise? (I'm assuming the damage caused will be mainly due to amount of force and not the duration)

   
   


2. 
   

   Assume you jump head first and hold a sharp and strong long object that cuts the water before you arrive, will that make the entrance to the water more smooth and protect you?

   
   

Answer

Answering your questions in reverse order:

Yes, a long pointy object (like your arms over your head, in a dive, or your pointed toes in a feet-first entry) will make a big difference. Remember the tongue-in-cheek adage, "it's not the fall that kills you; it's the sudden stop?" That is exactly what differentiates a fall onto concrete from a fall into water: how sudden is the stop. And making that stop LESS sudden (decreasing the magnitude of deceleration during the stop) is exactly how airbags save your life in a car crash. One can decrease the magnitude of deceleration by reducing the ratio $(\Delta V / \Delta t)$. Since there is roughly a linear relationship between time and distance traveled during the instant of impact, you can achieve the same effect by reducing the ratio $(\Delta V / \Delta s)$ where $s$ = distance traveled during the deceleration event. The easiest way to do this is to lengthen $s$.

One thing to remember about the water fall statistics is that a large number of them are likely "unpracticed". These are not olympic divers working up to 250 feet. A large proportion of them are unconditioned people forced into a water "escape"; or, worse, are people TRYING to die.

Assuming you are doing the right thing, and optimizing your form for water entry, you will simultaneously be minimizing your wind resistance during the fall:

1.) A fall from 30 feet will result in a velocity of roughly 44 ft/s = 30 mph.

2.) A fall from 100 feet will result in a velocity of roughly 80 ft/s = 54 mph.

3.) A fall from 150 feet will result in a velocity of roughly 97 ft/s = 66 mph.

4.) A fall from 250 feet will result in a velocity of roughly 125 ft/s = 85 mph.

The first case is a tower jump I did for the Navy, and is trival for anyone who is HWP and doesn't belly flop. The second is an approximation of a leap from a carrier deck, which the tower jump was supposed to teach you how to survive (be able to swim after the fall). The third is only 20% faster entry speed (and force) and should be survivable by anyone in good shape and able to execute good form (pointed toe entry, knees locked, head up, arms straight up). The La Quebrada cliff divers routinely dive from 125 feet as a tourist attraction. If forced to choose, I'd pick a feet-first entry at 150 feet over a dive at 125.

So the interesting part is the stretch from 150 to 250 feet. My guess is that the limit for someone voluntarily performing repeated water dives/jumps from a height of $x$ will show $x$ to be somewhere around $225 \text{ feet} \pm 25 \text{ feet}$.

EDIT: There are documented cases of people surviving falls from thousands of feet (failed parachute) onto LAND. These freaky cases of surviving terminal velocity falls do not answer the question practically; but they are there. For example, Vesna Vulović is the world record holder for the biggest surviving fall without a parachute.