Wikipedia:Reference desk/Archives/Mathematics/2012 April 3

= April 3 =

Car accident
I was sitting at a traffic light (in neatral,handbrake off)and was hit from behind. My vehicle travelled 7m and the vehicle that struck me 4m. If I know the weights of both vehicles (and the time elapsed if required)how can I calculate the speed of the vehicle that struck me at impact. — Preceding unsigned comment added by 2.26.160.145 (talk) 11:00, 3 April 2012 (UTC)


 * I don't think this is solvable, because it depends on the friction that both vehicles experienced. Without friction, the vehicles would never stop moving (or at least one of them). The vehicle behind you was likely using the brakes. The only way you could solve this is if you knew the velocity of both cars immediately after the collision. -- Lindert (talk) 15:32, 3 April 2012 (UTC)


 * Agreed, and you would also need to know if the ground was level, and, if not, the angle. StuRat (talk) 18:28, 3 April 2012 (UTC)
 * You may experiment on a quiet road to find the acceleration as your car slows down. Draw a line on the road with chalk. Drive slowly and put your car in neutral when reaching the line. Read the speed v when crossing the line (m/s). Measure the distance s before the car stops (m). Then compute the average acceleration a (m/s2) from the equation as=v2/2. Assuming constant acceleration, set s=7m&minus;4m in the equation and compute the speed of your car as the push from the other car ceased. Bo Jacoby (talk) 06:51, 4 April 2012 (UTC).
 * In all, with certain plausible assumptions and measurements, you may be able to find a rough estimate of the car's velocity when it hit you. From the description, it sounds as though the other car was not braking significantly (it travelled more than 50% of the distance your car did with minimal friction on yours); one could work from this hypothesis to produce a plausible scenario.  Bo Jacoby's suggested measurement, the slope, the law of conservation of momentum and these assumptions, you should be able to deduce a plausible figure.  — Quondum☏✎ 07:42, 4 April 2012 (UTC)
 * The car behind would not have shunted for 4m, but it wouldn't have been like a billard ball either because of the crumple zone which would absorb some of the energy. So momentum is conserved except for friction but energy is not. There might be some accident site on the web which would allow one to estimate the speed from what happens with actual cars. If you consider it as probably more like an inelastic collision asnd the cars were roughly comparable in weight then they were probably going at something like twice the speed you'd calculate using 7m I think. Dmcq (talk) 08:36, 4 April 2012 (UTC)

A level differentiation problem
f(x) = (1-x)^2.ln(1-x). I got f'(x)=-2(1-x).ln(1-x) - (1-x)^2 / (1-x), cancelling the second term to 1+x. The question actually asked for the second derivative at a particular point, which I got wrong in the book's answers, but would have got if the term was + (1-x)^2 / (1-x). Sketching a graph of ln(1-x) has a negative gradient for all x, so the book is right, but where is my use of the chain rule (as I think I've done it) wrong. Many thanks in advance for the replies. — Preceding unsigned comment added by 109.150.16.91 (talk) 14:36, 3 April 2012 (UTC)


 * The (1-x)² / (1-x) ratio does NOT cancel to (1+x) — (1-x²) / (1-x) does, but (1-x)² / (1-x) cancels to (1-x). --CiaPan (talk) 14:59, 3 April 2012 (UTC)


 * Doh! What a tit (OP here).  Many thanks.  — Preceding unsigned comment added by 109.150.16.91 (talk) 15:50, 3 April 2012 (UTC)

Hull
Noting the entries at Hull I wonder if someone could supply a definition for Hull (mathematics) (and given my low level of knowledge, perhaps even create a stub?). Thanks.Oranjblud (talk) 20:18, 3 April 2012 (UTC)


 * Are you looking for convex hull? Or do you mean something else? SemanticMantis (talk) 21:51, 3 April 2012 (UTC)
 * The page Hull lists several forms - I assumed these subtypes are not all sub-types of convex hull - eg Skolem hull is there an accepted definition of the term "hull" in maths?213.249.187.63 (talk) 22:41, 3 April 2012 (UTC)
 * To your last question: I think not, though I welcome correction :) There may be relations among a few of the various hulls, but as you say, they are not all subclasses of one or the other. I guessed convex hull because I think of that as the most commonly used concept, but that is of course subjective. Like ring or field, I think hull is just an English word that has been co-opted into special service in math, perhaps to serve as an analogy or source of intuition. But usually (always?) in math, "hull" appears with an adjective to specify which concept is meant. I've never heard "hull" used in math talks or texts without an antecedent adjective (perhaps implicit after introduction). SemanticMantis (talk) 01:59, 4 April 2012 (UTC)
 * I think that's a good exposition, and I would further add that, while there may be commonalities among different sorts of hulls (both the convex hull and the Skolem hull, for example, are closures of sets under a certain collection of operations), it would be a very bad idea to abstract those commonalities and write a Wikipedia article about them. It would be a form of original research, in the Wikipedia-term-of-art meaning of that phrase.  If hull, as a term expressing those commonalities, ever becomes an accepted part of mathematical terminology outside of WP, then we can write an article about it. --Trovatore (talk) 02:33, 4 April 2012 (UTC)
 * Thanks.Oranjblud (talk) 15:41, 4 April 2012 (UTC)
 * As far as I know, "hull" generally means "the smallest structure of type X which contains A". The convex hull of a set of points is the smallest convex set containing it; the injective hull of a module is the smallest injective module containing it; and so on. -- Meni Rosenfeld (talk) 17:48, 4 April 2012 (UTC)
 * Yes I guessed it would approximate to a 'mimimally containing set' (whatever that means). It does look as if no-one has formalised the definition in a way that could be referenced on wikipedia, as Trovatore says. Math/wolfram simply disambiguates http://mathworld.wolfram.com/Hull.html - it usually has a definition if a definition exists.. Not a problem - less work for me.Oranjblud (talk) 23:07, 4 April 2012 (UTC)
 * In my experience, MathWorld puts definitions even when they don't exist. "Exist" in the sense of being recognized usage, anyway.  That's perhaps my biggest criticism of the whole project, and it's something we need to be very vigilant about avoiding on Wikipedia. --Trovatore (talk) 06:53, 9 April 2012 (UTC)