DarkBlueChocobo
  • DarkBlueChocobo
Help with application problem
Mathematics
schrodinger
  • schrodinger
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DarkBlueChocobo
  • DarkBlueChocobo
A paddle boat is traveling down a lake at 15 mph. If the paddle wheel is 8 ft in diameter, how many revolutions per min is it rotating
DarkBlueChocobo
  • DarkBlueChocobo
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DarkBlueChocobo
  • DarkBlueChocobo
so the radius of the wheel is 4 ft then

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DarkBlueChocobo
  • DarkBlueChocobo
but first wouldnt we have to change units
DarkBlueChocobo
  • DarkBlueChocobo
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DarkBlueChocobo
  • DarkBlueChocobo
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DarkBlueChocobo
  • DarkBlueChocobo
Doesn't this give us the angular speed?
DarkBlueChocobo
  • DarkBlueChocobo
zepdrix
  • zepdrix
Umm umm umm, I'm getting a little confused by your break down of the units. Lemme show you how I'm thinking about it.\[\large\rm boat~speed=\frac{15\color{orangered}{(miles)}}{1\color{royalblue}{hour}}=\frac{15\color{orangered}{(5280ft)}}{\color{royalblue}{60\min}}\]So we get that the boat travels at a rate of:\[\large\rm boat~speed=\frac{15(5280)}{60}\frac{ft}{\min}\]And the circumference of our wheel is:\[\large\rm C=\pi d\qquad\to\qquad C=8 \pi ft\]The distance around the wheel, the circumference, is `one full revolution`. So our wheel is moving at this rate:\[\large\rm wheel~speed=8\pi\frac{ft}{rev}\] So then ummmmm, we divide I guess? \[\large\rm \frac{15(5280)}{60}\frac{ft}{\min}\div8\pi\frac{ft}{rev}\]Sorry I'm a little rusty on these types of problems :) lol
zepdrix
  • zepdrix
\[\large\rm =\frac{15(5280)}{60}\frac{\cancel{ft}}{\min}\times\frac{1}{8\pi}\frac{rev}{\cancel{ft}}\]
zepdrix
  • zepdrix
Mmm I need a brief refresher on this stuff XD What is this type of problem called? I'll Google it. Something with rotational motion?
DarkBlueChocobo
  • DarkBlueChocobo
Well the beginning of it was Angular speed and then you converted it to linear speed basically because they are related
zepdrix
  • zepdrix
I guess I made it a little bit of extra work by writing the angular relation like this. I should have written it like this: \(\large\rm \dfrac{1rev}{8\pi ft}\) And then it's just a multiplication problem, canceling out the units in the long string as you did.\[\large\rm \left(\frac{15miles}{hr}\right)\cdot\left(\frac{5280ft}{mile}\right)\cdot\left(\frac{hr}{60\min}\right)\cdot\left(\frac{1rev}{8\pi ft}\right)\]
zepdrix
  • zepdrix
I think you just had your last term a little off, ya? :o The wheel spins 8pi every revolution.
DarkBlueChocobo
  • DarkBlueChocobo
It seems so :<

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