I am looking for an equation to which I can plug in numbers to figure out to what depth a person will sink into water before momentum is lost and they begin to float upwards, depending on how high they jump from.  To keep it simple, I am assuming 90 degree straight fall, feet first, and the position is kept in the water until momentum is lost.
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?
Novel where pyramids "grow" and change Earth's magnetic field? I read this in (most likely) the 1980s or 1990s. The protagonists found what they believed were alien spacecraft; over time, they &quot;morphed&quot; into Mesoamerican-style pyramids (stepped, not smooth like Egyptian pyramids). Each time they &quot;grew&quot;, an area where electrical equipment either failed or was unreliable grew; the pyramid itself became a new magnetic pole. It turned out that there were a dozen of these objects, spaced to cover the entire world from the corners of an icosahedron; the final morph of the pyramids caused the fields of electrical &quot;disablement&quot; to cover the entire world. Why does $k/m=\omega^2$ for harmonic motion? Can anyone please give me a proof for $k/m=w^2$ in simple harmonic motion?  I have tried energy conservation and Newton's laws as follows :  In the case of a mass-spring system,  $$F=ma =-kx\\ F=ma = mr\omega^2 $$  hence   $$\frac km  = \omega^2$$  Or   $$\frac12 mv^2 = \frac12kx^2$$  $$\frac km  =  \frac{V^2}{x^2}   =   \omega^2$$  therefore $k/m  =  \omega^2$  Are these valid and correct? I have been stuck in this for the  entire day. User deleting code after question has been answered If a user keeps  (thus making the answer meaningless), what should we do? Rollback the edit (what if the user just deletes the code again)? Delete the question?  More examples (same user): ,  (see also edit histories). I flagged a post today, typed out a fairly thorough explanation, clicked the button... and got told that I'd already flagged this post (for something else, which I'd forgotten about) so this flag wasn't allowed.  (This happens if the first flag is still active.)  The dialogue with my explanation was gone at this point, so if I wanted to communicate with the moderators about that, I was going to have to start over.  (In case you're wondering how this could happen, one flag was related to the post itself and one was related to the user -- there being no way to flag a user directly, you have to hang it off of a post.  But I've also seen this with cases where the first flag hangs around unhandled for a week or two and I've forgotten about it.)  Since the system is going to detect that I've already flagged a post and reject a second flag, can it do that after I click the "flag" link instead of waiting until the end of the process?  (Or gray out the link so I can't click it in the first place?)  2015-12-18: someone suggested to me in chat today that this had been implemented, so I tested again.  The behavior has not changed: I flagged a post using "other", then flagged it again (also "other") before the first flag was handled, and the flag was rejected only after I'd typed the message.  (I did this on a site where I'm a moderator so I could then clean up after myself.) Export each image from a collection in Google Earth Engine Proof of dividing fractional expressions For dividing two fractional expressions, how does the division sign turns into multiplication? Is there a step by step proof which proves  $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}=\frac{ad}{bc}?$$ What is the shortcut for opening a new window (opening folders). for that I have to go to folder options and right click and then need to click on open new window.  or I have to make focus on the folder icon or open a folder then press  Ctrl+N  for opening a new window is there any direct command spcific to open a new window in ubuntu. How to find historical stock price for a de-listed or defunct company? With services like Google Finance or Yahoo Finance it is very convenient to find the historical stock price metric of a listed company, but if the company is not listed, I can't find the data.  For example, I want to see the price metrics for Macromedia, which had been listed in 1993 on NASDAQ (MACR), then acquired by Adobe in 2005. How could I find its historical price metrics? A Basic Question about Gravity, Inertia or Momentum or something along those lines Let $a,b$ be positive integers.  When $$k = \frac{a^2 + b^2}{ab+1}$$ is an integer, it is a square.    Proof 1: (Ngô Bảo Châu): Rearrange to get $a^2-akb+b^2-k=0$, as a quadratic in $a$ this has two values: $a$ and $kb - a = (b^2-k)/a$. (The second root is determined in two different ways from the expansion $(x-r_1)(x-r_2) = x^2 - (r_1 + r_2)x + r_1 r_2$.)  Now suppose we have $a,b$ such that $k$ is an integer but not a square, by the investigation about roots we have that the second root is a nonzero integer since $k,b,a$ are integers and $k \not = b^2$, futhermore it is positive which is easily seen from its defining equation.  WLOG assume $a \ge b$ so that the second root is strictly smaller than $a$. This leads to a decent, replacing $a$ with the second root.    Proof 2 (Don Zagier): Apply reduction theory (specifically, Sätze 1 and 2 of Section 13 of my book on quadratic fields) to the quadratic form $x^2 + kxy + y^2$, which is the unique reduced quadratic form in its equivalence class.    Note that Proof 2 is pretty much the same as Proof 1 when written out in explicit detail, but I could not read Zagier's book because I cannot read German.  I would like to know more approaches to this and other alternative proofs of this result if possible! Thanks in advance.  I would also be interested in related problems (especially easier ones of a similar nature) and texts which cover the reduction theory in English. How to repair a broken .EXE file association Can a level 1 Warlock Cast a 4th level spell from 8th level Sorcerer with their warlock pact magic spell slots? Can my player’s multiclass Warlock 1/Sorcerer 8 cast the higher level sorcerer spells from with their warlock pact magic spell slots?  My player argued that he could now cast his 4th level sorcerer spells with his level 1 warlock  spells slots. I think he interpreted pact magic as "highest spell slot possible",  so he figures that since he has 4th level spell slots, he interprets that the warlock spell slots are 4th level slots now too. I have a notebook with no Scroll Lock key (or any shortcut using the 'Fn' key).  Somehow Excel 2010 got the Scroll Lock on. I see it left down in the status bar and now I can't navigate through cells using the arrow keys, which is pretty annoying. It wasn't turned on some hours ago, so I think I must have hit some Scroll Lock toggle shortcut in Excel 2010 by mistake.  Anyone knows what hot to turn off Scroll Lock in Excel (shortcut or menu option)? How to get the Runtime-Type of an Object dynamically (for Primitive Data Types and SObjects) Is it possible to get the Type of an Object (it's not an SObject)?  String s = 'test'; doSomething(s);  public static void doSomething(o Object) {     // need to find out if o is a string or an integer     type = IsThereAMethodToGetTheTypeOf(o) // ?     if(type='String') {         // do something for strings here ....     } else {         // do something else ....     } }   I think the Type class can't help me, because it has no way to get the type of an existing object instance, right? Any there any other way?  Since there is most likely no perfect solution possible within the current platform limitations, I posted an Idea on IdeaExchange here:   For SObject I have already this  public static string getType(SObject obj) {     if(obj==null) return '';     return obj.getSObjectType().getDescribe().getName()+''; } Fiction novel or movie about sentient dinosaurs I remember parts of a story about some researchers finding a society of sentient dinosaurs. I believe they lived underground. From what I recall there were some steam punk elements and I think crystals were important.  From what I recall (this might be wrong) there was a book and also a movie about that story.  In the process, humans lived with these dinosaurs. I am not sure if that was like that from the beginning or if that happened later.  Any idea what that story might be? I have a Toshiba satellite A-200 laptop with a Vista OS on it with 4 NTFS partitions  (C:) Vista  (D:) Entertainment  (E:) Work  (F:) Sources   and I wanted to start using Ubuntu instead. So I tried it first from the live CD and everything was OK and all the partitions were shown and working and so I decided to install Ubuntu to replace Vista on the (C:) drive. After I did that I can no longer find my folders and files on the (D:), (E:), (F:) partitions and the only file system that is shown is one 198 GB although my HDD is 320 GB.  I can't access the lost data on the remaining 120 GB which I hope is still there and not totally lost  I am now working from the live CD but I am unable to install testdisk. Can I recover the Vista partitions by the product recovery CD to get my laptop back to the factory settings? Can I recover the NTFS partitions using a recovery program for Windows or will that make the problem worse?   I need these data badly as I don't have a backup for them. Finding joint density of dependent variables I've got two random variables, $x$ and $y$, where $x=u(y)$ and $y=v(x)$. How do I find the joint density of the two variables?   The eventual purpose is to find the integral  $\int^a\int^b f(x,y) dydx$,  where $f(.)$ is said joint density function.  This question is related () but I'm still a bit confused by the answer. I am indeed effectively looking for $Prob(x \leq a, y \leq b)$ but don't understand how I can get there without knowing the PDF first.  Any advice is much appreciated. Thanks a lot in advance! Importance of PTR records on nameserver IP's? I have not yet experienced any DNS failures due to a missing PTR record, but am wondering:   Is there any added value in having a valid PTR record on a nameserver IP-address? How to access raw texture data in DirectX 11? I want to get access to a texture's pixel color data on the CPU. When trying to map the texture, I get E_INVALIDARG in return from ID3D11DeviceContext::Map.  ID3D11ShaderResourceView* resourceView; //represents my texture, already loaded up //...  //Getting the resources of the texture view... ID3D11Resource* res = nullptr; ID3D11Texture2D* tex = nullptr; resourceView-&gt;GetResource(&amp;res); res-&gt;QueryInterface(&amp;tex); D3D11_TEXTURE2D_DESC desc; tex-&gt;GetDesc(&amp;desc); //Correct data gets filled out D3D11_RESOURCE_DIMENSION dim; res-&gt;GetType(&amp;dim); //value gets set as Texture2D which it should  D3D11_MAPPED_SUBRESOURCE mappedResource; HRESULT h; h = context-&gt;Map(tex,0,D3D11_MAP_READ,0,&amp;mappedResource); //This always fails h = context-&gt;Map(res,0,D3D11_MAP_READ,0,&amp;mappedResource); //This also fails   The idea is that I keep only shaderResourceViews for my textures, because that is all I needed until now, and get the relevant resources here.  I tried mapping as WRITE_DISCARD also, but to no success. I am really confused, because I never had any problem with mapping constant buffers and vertex buffers. I seem to be certainly missing something? By the way, I am using Wic Texture loader and DDS Texture loader for the DirectXTex toolkit, and tried this code for png, dds textures, with and without mip-maps. In a bash shell script, writing a for loop that iterates over string values In bash, I know that it is possible to write a for loop in which some loop control variable i iterates over specified integers.  For example, I can write a bash shell script that prints the integers between 1 and 10: #!/bin/bash  for i in {1..10} do  echo $i done  Is it possible to instead iterate over a loop control variable that is a string, if I provide a list of strings?  For example, suppose that I have a string fname that represents a file name.  I want to call a set of commands for each file name.  For example, I might want to print the contents of fname using a command like this: #!/bin/bash  for fname in {&quot;a.txt&quot;, &quot;b.txt&quot;, &quot;c.txt&quot;} do  echo $fname done  In other words, on the first iteration, fname should have the value fname=&quot;a.txt&quot;, while on the second iteration, fname should have the value fname=&quot;b.txt&quot;, and so on.  Unfortunately, it seems that the above syntax is not quite correct.  I would like to obtain the output:  a.txt b.txt c.txt  but when I try the above code, I obtain this output:  {a.txt, b.txt, c.txt}  Can you please help me determine the correct syntax, so that I can iteratively change the value/contents of the variable fname?  Thank you for your time.