How deep can I go if jumping from 50m?
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1$\begingroup$ This depends a lot on what you do once you're in the water. For what it's worth, I've jumped into a deep lake from probably 30m high and hit the freezing cold thermocline. It was shockingly cold and I started to panic because I went way deeper than I expected and swimming to the surface seemed like it took forever. $\endgroup$– Brandon EnrightCommented Aug 16, 2014 at 9:24
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1$\begingroup$ Apparantly at around 50m even the pros break bones. See chart of records in en.wikipedia.org/wiki/High_diving $\endgroup$– Brandon EnrightCommented Aug 16, 2014 at 9:40
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1$\begingroup$ @BrandonEnright And on a related note, there's also shallow diving (incidentally, this is how I understood the question in the first place): en.wikipedia.org/wiki/Shallow_diving $\endgroup$– alargeCommented Aug 16, 2014 at 9:50
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1$\begingroup$ If you watch underwater camera takes of high divers, you'll see that they quickly "curl" off vertical after going submerged. As everyone's pointed out, surviving the initial impact is the hard part. After that, proper subsurface angling will bring you to a stop in (WAG) 10 meters or less $\endgroup$– Carl WitthoftCommented Aug 16, 2014 at 14:15
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2 Answers
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First one can get killed even by coming in contact (with speed from high altitude) with the water surface, which at this speed and momentum it appears as a "block of cement" (or more correctly, develop high enough forces to break your bones as per @dmckee's comment).
This depends what wil be the impact surface (that is why seals and olympic divers fall into water with a minimum surface of impact, i.e perfectly vertical).
Then the height (or depth) necessary is found by knowing the altitute of fall, plus the weight of the body. This enables to find momentum at time of impact with the water surface.
Momentum at time of impact plus the buoyancy factor of the water (which depends on amount of salt among others) gives the depth the body will reach. Then the safety depth is that depth by adding a safety margin (if you want an engineering approach and not just physics one)
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$\begingroup$ This is too simplistic. You are neglecting the work done by the falling body in displacing the water, which will appear at large distances as both body waves and surface waves, plus in uplifting some water above the unperturbed water level. This work is provided by the falling body's kinetic energy, and this portion of KE need not be counteracted by buoyancy any more. $\endgroup$ Commented Aug 16, 2014 at 10:42
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$\begingroup$ @MariusMatutiae, you are only partially correct (and by a small amount), in the answer it specifically mentions perfectly vertical impact, as such minimum amount of water thrown off (which in a sea or ocean does not make such a difference). So this is not as simplistic as you would make it seem. If the OP wants to provide specific numbers, specific calculations can be done, else answer follows the spirit of the question. Simple as that but not simplistic. $\endgroup$– Nikos M.Commented Aug 16, 2014 at 10:45
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$\begingroup$ Thanks for your comment, Nikos, it illustrates powerfully my concern. You obviously make no distinction between streamlined and non-streamlined bodies (a dish and a pencil of the same weight need different depths) and obviously neglect horizontal water displacement, as if a ship could sail effortlessly into the sea. $\endgroup$ Commented Aug 16, 2014 at 10:57
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$\begingroup$ @MariusMatutiae, sorry, dont see how this comes about? who said that a pencil and a dish will have same depth? certainly not me? In any case the answer involves perfectly vertical impact of body, as an olympic diver, feel free to add another answer $\endgroup$– Nikos M.Commented Aug 16, 2014 at 11:00
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$\begingroup$ Thank you for your gracious suggestion. There is horizontal displacement of water also for idealized vertical impact. $\endgroup$ Commented Aug 16, 2014 at 11:05
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Assuming you do survive the impact with the water, according to this answer all you need is 4m.
