This may seem silly a lot but I really need some clarification on the necessity of escape velocity for a rocket leaving the Earth's gravity. A stone thrown vertically upwards reaches to a certain height before falling to the ground. The height at which the total potential energy gained by the stone is equal to the sum of the kinetic energy at the ground and the work done on it during launch. Since, after throwing it upwards, no external work is added, the stone WILL return to the ground in accordance with the law of energy conservation (velocity &lt; escape velocity). But in a rocket, continuous work is being added from its booster motors. Then why is it necessary for it to acquire escape velocity in order to leave the Earth? What will make it stop from leaving? Consider the following hypothetical case:  A hypothetical situation:  Suppose we build a long vertical shaft on the Earth's surface, reaching into deep space and a person starts climbing on it (just like Jack on a bean stalk). Will he also require escape velocity to leave the Earth's gravity? If no, then how is it any different from a conventional rocket launch?  Please answer!
The escape velocity of earth is roughly $11 kms^{-1}$. However, what if a long ladder was built extending out of Earth's atmosphere and considerably more. Then if something was to climb up at much less than the escape velocity, what would happen when it reached the end?  And what if the object that climbed the "ladder" then fired some kind of thruster/rocket and was going fast enough so that it orbited the Earth. It would mean less energy required to get into orbit?
Removing the password from a PDF file I have a couple of ebooks as PDFs with passwords, however my ebook reader (sony prs600) doesn't seem to support PDFs with passwords.  What is the easiest of removing the password from a PDF (I know the password, which presumably helps a lot).  It's a bit annoying buying a book and then only being able to read it in front of a computer. I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference? Can a Windows virus transfer to Ubuntu? How to match all occurrences of a regex How to increase the width and height of the Rich Text area field in Visual force Page? "I have never said" versus "I never said" I have never said this.   I never said this.    Is the usage of have in the first sentence justified or grammatically correct?   What is the difference in meaning?   When should I use one form over the other? Allow moderators to see delete/undelete activity on users' profiles We get auto flags for 'possible vandalism' related to deletes, and these can be helpful at times in finding 'rage quit' users, or other potential problems.  But often, I would like to know if there is a prior pattern with the user doing this. While we can see posts of theirs which have been flagged, and perhaps find previous auto flags this way, it would be nice to see an overall view of their self-deletions and undeletions; mostly just to identify patterns.  Such a feature would be nice if it was activity centered, rather than post-centered. That is; each delete/undelete action should be shown. So we could easily see, for example, if someone went back-and-forth on a single post.  The "activity" tab in the profile would be a logical place to show these events.  I think this would be best to be limited to instant self-deletions, not deletion votes. As linguistics student, I have to put more than one thing on a character every now and then. For example, I need to type ā̆. I thought I could simply do that by typing \={\u{a}}, but then the macron is placed above an empty space in front of the character.  How can I solve this? Thanks  P.S. I'm using MiKTeX 2.9, running on Windows 8; in case it might be of use. How do I join several objects into one? I'm creating side skirts for a truck and I am duplicating the frames I want. The problem is it's making the duplicated object into another object. How do I put it into the same one? I have two custom taxonomies applied to two custom post types. the terms list on the sidebar just fine and will list all posts associated with it. However, if you search one of the terms in specific, it doesn't bring up a post with that term.  Example:  Search for term "PQRI"  I get nothing. Any ideas? I've tried using various search plugins but they either break my custom search parameters or just don't work. Conflict between tkz-fct and thmtools? I recently upgraded to Snow Leopard, from Leopard and I was using an awesome app called  that let you remap your keys, set scripts/macros and even had repeat functionality.   However, this app doesn't seem to be in active development anymore, and 10.6 broke the ability to bind certain modifier keys (Shift) with other keys.   I totally miss things like Shift+Insert for paste (Linux/Windows), setting Ctrl+Shift+Esc for Activity Monitor, and Ctrl+Alt+Del for the login window.   So, how can I achieve this instead? Mounting Flashdrive - mounted to home directory I wanted to mount my flashdrive, and made the mistake of setting the mount path as /home/my_name. Now all of my documents, downloads, pictures, etc. are unavailable since my flashdrive has replaced my previous home folder.  When I go to terminal and type sudo umount /home/my_name I get the error message:   umount: /home/my_name: device is busy.         (In some cases useful info about processes that use          the device is found by lsof(8) or fuser(1))   Is there a way to fix this, where I can restore my old /home/my_name folder and then mount the flashdrive to a proper location? How to convert std::string to LPCWSTR in C++ (Unicode) ANOVA assumption normality/normal distribution of residuals Illustrating op amp feedback without control theory We are teaching op amps in a high school class, before calculus.  So we can't use control theory to teach how op amps respond.  All the same, I would like to have an intuitive explanation for how a feedback circuit works.  Take the negative feedback, for instance.  Is there a clear way to show how an initial difference of delta between V+ and V- leads to a very large (G(V+ - V-)) difference in the output, which then leads to ...  I'd like to be able to take that argument and show how the voltage of the output converges in addition to the standard virtual short argument.  Can anyone explain it clearly? Can space expand with unlimited speed? just after the Big Bang and before inflation the currently observable universe was the size of a coin. One millionth of a second later the universe was the size of the Solar System, which is an expansion much much faster than speed of light. Can space expand with unlimited speed? "None" as plural indefinite pronoun In my grammar book (English Grammar, HarperCollins Publishers), I read that none is occasionally treated as plural, but it is usually regarded as singular. Can you give me an example of sentence where none is used as plural pronoun? External Hard Drive no longer working I am on a MacBook Pro 13 running latest Sierra. I have an external Seagate solid state hard drive that was working and out of the blue stopped working. The only thing on it was my Adobe Lightroom images/videos. Not the LR DB files. I'm sure you have all heard this woe before, so I won't dwell on that. And yes, I back up to the cloud. AWS S3 specifically. Though I am traveling South East Asia for the last year, and staying in cheap hostels. So good internet is hard to come by sometimes. I can't back it up after every export. While most of it is backed up, there is some that is not.  Moving on. The symptoms seems to change every time I plug it in. The first sign was it ejected on it's own. I plugged it in again, and it wouldn't mount. Disk Utility recognized it, so did the command line diskutil list but it wouldn't mount. I rebooted and it worked for a second. Then I could only get to it from the command line. Then trying to frantically back up to my local what was not backed up to the cloud, it all failed. Basically just a cp -R [directory] [local-directory] command.  After some more frantic unplugging and re-plugging plus some command line manual mounts, I finally got it to where the Disk Utility would be able to run first aid on it. It failed. I don't recall the error. So I put it in a freezer. After a few hours I tried again. It is not any better. It still will not mount. Now Disk Utility sees it, but with no partition. I can't even give me information about how much space is used on it.  I have also tried it from a Windows machine. It did not mount. I have tried other cables. No success. As well as tried my other USB port. I also have another working external hard drive exactly like the one giving me issues. It works on all cables and USB ports.  I do have Docker running with a Ubuntu container, I'm trying to think of a way to see if I can try to get to the USB from there. I also have a USB that I have thought about running a live Ubuntu on there to see if I can mount and retrieve the data or fix the HDD that way. But if it will not mount, I doubt these will work.  Can anyone else think of any other tricks I can try myself to see if I can repair this or at least retrieve the data without paying for a service or software? If not, those suggestions are also welcome.  Update   I made the mistake in original post that it was a Solid State Drive. This is my mistake, it is actually a spinning disk hard drive. I bought them long ago and have been traveling with them for so long I just forgot. Question is updated to reflect this. Now diskutil list does not show it at all. The Disk Utility app also does not see it. Based on suggestion from @Allen I seeked out the USB to SATA cable. I did not quite find it, as my options are extremely limited where I am at. Though a local expat on a facebook group was able to help me with a empty 2.5 casing that I was able to extract the drive from original casing and put it in his blank case. It now mounts. Though it has the "click of death" sound to it. And data is not really reachable. While I can ls the directories and Adobe Lightroom does not have the exclamation mark when it can not reach the actual external files. Right clicking on the images and clicking on "Show in Finder" or any other variation of trying to get to the files through Finder or terminal, I have no success. It usually hangs and I get the spinning wheel. Since Adobe Lightroom imports these images into directories named by date, I am going to send the drive off to a data recovery service and ask to recover just unbacked up directories i.e. dates. Next time I will make harder efforts to backup and probably get an actual SSD.   I think this can be closed, due to my low reputation points I can not close this myself. Show that if $f:X\to Y$ is a continuous function if and only if the graph of $f$ is a closed subset of $X\times Y$