Re: [Math4u] Calculus Help

Rob:

My assumption is that we are interested in the velocity at which the beam moves along the shore.  Not clear though - I must agree.

Regards,

Rich B.

how fast is the beam moving  > when it passes you? > 

-----Original Message-----
From: Rob van Wijk <robvanwijk@gmx.net>
To: Math4u@yahoogroups.com
Sent: Fri, 2 Nov 2007 2:54 pm
Subject: Re: [Math4u] Calculus Help

 Comments inside:  -------- Original-Nachricht -------- > Datum: Wed, 31 Oct 2007 15:52:05 -0000 > Von: "luvmath03" <luvmath03@yahoo.com> > An: Math4u@yahoogroups.com > Betreff: [Math4u] Calculus Help  > I have just a couple of questions that are weirding me out.  I think  > I should be able to get them but the unit analysis is confusing me  > more.  I am just not really able to form the ininial equations and  > such.   >  > Question 1.   > A lighthouse is 1 mile off shore, due west.  You are on the shore 2  > miles north of the point opposite the lighthouse.  The light rotates;  > if you see the flash every 15 seconds, how fast is the beam moving  > when it passes you? >  > I have an answer of 2/2.625 miles/sec but I don't feel its write  > since I feel like I need to use the chain rule (section we are  > in)....How would I set up an equation to relate Theta and  x miles?   > when I  differentiate I have d(theta)/dt and I would solve for d > (x)/dt.    What you need differentation for anyway?  Right triangle with rectangular sides 1 mile and 2 miles, so Pythagoras gives me a hypothenuse (and therefore a radius of the circle the light spot move along) of: 2,2360679774997896964091736687313 mile  If that's the radius, then 2 pi * radius gives a circumference of that circle of: 14,04962946208145278631274928641 mile  Since you see the light every 15 seconds the light spot travels at: 0,93664196413876351908751661909399 mile/sec  (Delibaretly sketchy, you should be able to fill in left-out pieces of /why/ this works yourself. If not, let me know.)   > Question 2.   > A trough is triangular in cross section, an isosceles triangle with  > sides of 12 inches and a top of 10 inches.  The trough is 40 inches  > long.  How fast is the depth change if you are pumping 1 cubic  > foot/min into the trough.  I know the answer will depend upon the  > height of the liquid at an instantaneous time (t).  I think I kind > of have this one but just want to see another thought.    Just out of curiousity, what is your answer? It would be much better (from a teaching point of view) to give you a subtle hint where the error in your calculation is than to just give the answer.  > Question 3.  > I am really lost here.   > A light is attached to a 13 in radius bicycle tire, at a point 8  > inches from the center.  If Harvey rides the bike at 15 mph, how fast  > is the light moving up and down at its fastest.   >  > I know the light is at a point that is horizontal to the road for the  > fastest up and down point.  Determine the revolutions per second of the wheel (given the radius of the wheel and the speed (I feel sorry for you; you'll have to convert inches to miles or the other way around, in the metric system this'd be a lot easier) then you get an angular speed which you can convert to a "straight speed" using the distance between axle and light.  > Thanks in advance for assistance.   > William  Good luck, Rob  --  GMX FreeMail: 1 GB Postfach, 5 E-Mail-Adressen, 10 Free SMS. Alle Infos und kostenlose Anmeldung: http://www.gmx.net/de/go/freemail     Yahoo! Groups Links  <*> To visit your group on the web, go to:     http://groups.yahoo.com/group/Math4u/  <*> Your email settings:     Individual Email | Traditional  <*> To change settings online go to:     http://groups.yahoo.com/group/Math4u/join     (Yahoo! ID required)  <*> To change settings via email:     mailto:Math4u-digest@yahoogroups.com      mailto:Math4u-fullfeatured@yahoogroups.com  <*> To unsubscribe from this group, send an email to:     Math4u-unsubscribe@yahoogroups.com  <*> Your use of Yahoo! Groups is subject to:     http://docs.yahoo.com/info/terms/   

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