-------- 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
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