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Hi Sudha.I am taking velocity to have 2 components, namely, magnitude ( u ) and the angle of projection (Q) .R = u^2 sin(2Q)/gHere, we call it range and not simply the horizontal displacement since: 1) if I keep u constant but change Q the horizontal displacement is going to vary between 0 and a maximum value R(=u^2/g).2) now if I keep Q constant and change the value of u then also I'll get varying horizontal displacement ( directly proportional to u^2 ).Enjoy !

Not much difference as both share one classic component , namely dealing with many horrible people ….have u been travelling lately ? Blame the low cost airlines : result: low cost customers who on the whole make more damage than good

Sadly, I think this is going to be tough. I don't think I'll be able to give constructive tips on how to read Indian names better, but I can give an idea of the common mistakes, the root causes for those, and maybe that will help.The rest of this answer is written based on my experience of Americans (mis-)pronouncing Indian names. I believe most of these comments will apply to other English-speaking peoples, however, they might probably not apply to people who speak other languages. Note also, that for pronounciations, I will try to give an informal pronounciation, followed by the IPA (http://en.wikipedia.org/wiki/Wikipedia:IPA_for_English) pronounciation (to the best of my abilities - I am not an expert in IPA, and particularly, I am likely to make mistakes in the stresses.)Stress: One big difference between English and Indian languages is that the former have stressed and unstressed syllables, whereas the latter have just long and short syllables. Due to this every Indian name sounds different when pronounced by an American. Take my name (Navin) for example. An American instinctively tries to guess which part is stressed. If she assumes that the first part is stressed, she will pronounce it as NAY-vin (neɪ'vɪn). If she assumes that the second part is stressed, whe will pronounce it as nuh-VINE (nʌ.vaɪn'). Even when I point out that my name is pronounced nuh-vin (nʌ.vɪn), they will usually end up pronouncing it nuh-VEEN (nʌ.viːn') or in the best case nuh-VIN (nʌ.vɪn').It is a difficult concept for an American to grasp that words can be said without stressing any specific part of it.Vowels: The biggest culprit here is 'a' and to some extent 'i'. The main problem here is that we (Indians) have been particularly bad about transliterating different sounds to the same English vowel. Thus the sounds UH (ʌ), AA(ɑː) and AY(eɪ), and E(ɛ) all could be transliterated to just a single 'a' in different names. And, sadly, there is no good way for you to know a priori which is which. We (Indians) know this because we have heard the correct pronounciations hundreds of times before (or we have seen the name in one of the original Indian language scripts which does a much better job of preserving the prounounciations). Thus, for example, the 'a' in Navin is an UH(ʌ) but in Rajesh it is AA (ɑː). One of the most common errors Americans make is mixing up these two, and I don't know of a good way you can fix this.A bit easier is 'i'. Americans have a tendency to pronounce it like the I in VINE (i.e. aɪ). However, in most Indian names, it is likely to be a short i (like the i (ɪ) in kid (kɪd)) or a long i (like the ee (iː) in feel (fiːl)). The difference between the two is not so great, so as long as you pick one of the latter two pronouncations for 'i', you should be OK.On encountering a 'u' most Americans pronounce it as UH (ʌ) as in cut, but. However, in most Indian names, 'u' is to be pronounced as in put (ʊ).An 'e' at the end of an Indian name is usually meant to be pronounced (unlike the "magic e" at he end of English words/names). Thus Gore, More, Pore are all Marathi surnames that are pronounced go-ray (gorɛ), mo-ray (morɛ) and po-ray (porɛ).In most other cases, vowels are not a problem.Consonants: Here, the main problem is that Indian languages have a whole bunch of sounds that Americans don't notice the difference between. To get an idea of this, check out What is the difference between these Hindi words that I'm unable to hear?Specifically, as indicated in the answers to that question, 't' has two different sounds - the normal t and the t̪. 'd' can either be pronounced as in dog (d) or as in the (ð). In addition, most consonants have an aspirated form, and usually Americans are not good at noticing the differences between the two. Thus, k and kh are different sounds, and so are g and gh, ch and chh. This becomes even more problematic when you think about th (which can stand for the aspirated form of t or t̪ - so that makes 4 sounds that most Americans think are one). And this becomes much worse when you consider that North Indians and South Indians use different conventions to transliterate the four 't/th' sounds. North Indians use 't' to represent either t or t̪ and they use 'th' for the aspirated forms of those two sounds. However, South Indians use 't' for the 't' sound and 'th' for the t̪ sound. I don't know what they use for the aspirated versions.The only good news in this sordid tale is that most of the long names are usually just concatenations of shorter names taken from a fairly limited vocabulary. South Indian names (which are usually just concatenations of names of Gods) and Sanskrit names in religious texts (which are usually just combined words), and the two main sources of long names. Typical North Indian names of people are usually short.In cases of these combined names, you would need to know the vocabulary to be able to break up the names. Here is a starter set to get you started on South Indian names:Rama - raam (rɑːm)Laxmana or Lakshamana - laksh-mun (lʌkʃmʌṇʌ) - Note: the correct prounounciation of the 'ṇ' is beyond the scope of this answer. You should be able to get away by prounouncing it as n. Sometimes shortened to Laks (but this is not very common)Laxmi or Lakshmi - laksh-mi (lʌkʃmɪ)Krishna - krish-naa (krɪʃnɑː) at the end of the word or krish-nuh (krɪʃnʌ) elsewhere. Often shortened to Krish or Kris.Swami - svaa-mi (svɑːmɪ). Sometimes simplified to sami.Venkat - ven-kuht (vɛŋkʌt) - Often shortened to Venky.Venkatesh - ven-kuht-aysh (vɛŋkʌtɛʃ) - Often shortened to Venkat or VenkyVenkateshwara - ven-kuht-aysh-war (vɛŋkʌtɛʃvʌr) - Often shortened to Venkat or VenkyAnand - aa-nuh-nd (ɑːnʌŋð)Vijay - vij-aye (vɪ.dʒʌj) Note: the j at the end there is the 'y' sound which needs to be pronounced in full. Most Americans pronounce this vi-jay (vɪ.dʒeɪ), which is wrong.Viswanath - vish-vuh-naath (vɪʃ.vʌ.nɑːt̪h) - Sometimes shortened to Vish.Narayan - naa-raa-yun (nɑːrɑːyʌn) - Rarely shortened.Murthy - moor-ty (muːrt̪ɪ)Siva - shee-vaa (ʃiːvɑː) if at the end of a word/name or shee-vuh (ʃiːvʌ) otherwise. Sometimes, it might be shortened to Shiv (ʃɪv).In most of the above, you can also add an optional 'an' if it occurs at the end of the word/name. So you get Vijayanarayanan Ramamurthy and Viswanathan Anand. So the name you mentioned, you can now break it up as Lakshmi + Narayan + an and Renga + Narayan + an.Also, note that in case of many South Indians use just the first component of the name and use that for normal day-to-day conversation instead of the whole name. Hence, Sivaramakrishnan will usually call himself Siva. I had a professor (Raghu Ramakrishnan) who used to say that his name was Raghu and the rest of it was just the checksum. (He stole this line from someone else whose name I don't remember because it was too long).Also remember that many South Indian names contains initials (like P.T. Usha) and while the full name (Pilavullakandi Thekkeparambil Usha) might be used in formal settings (e.g. as listed authors in a paper) in most cases, the initials are not expected to be expanded, and leaving the initials initialized is the right thing to do.For the Sanskrit names, I think you'll need to learn Sanskrit to be able to see where they break. For example, in ashvamedhika, I happen to know that 'ashva' stands for horse, so I break it up at 'ashva-medhika' (and in fact I happen to know that 'ashvamedh' is the word for horse-sacrifice, hence I can easily remember the whole too). Similarly in ashramavasika, I know the word 'ashram' and I know that 'vasika' means dweller, so that is how I break that up. And so on. The only good news is that most translations of Indian religious and historical texts (at least the printed ones) will use a standardized transliteration scheme, and will include a pronunciation guide at the beginning, which makes it easier to see the pronunciations.