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anonymous
 one year ago
The beacon at the airport is located 300m from a straight runway ay its least distance. The beacon rotates 10times per minute, how fast is the beam of light moving along the runway when the beam is 700 from the closest point to the beacon on the runway.
anonymous
 one year ago
The beacon at the airport is located 300m from a straight runway ay its least distance. The beacon rotates 10times per minute, how fast is the beam of light moving along the runway when the beam is 700 from the closest point to the beacon on the runway.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433048694364:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If your drawing is correct, you should just use the algorithm of Pythagoras to solve it: \[a^2+b^2=c^2\]dw:1433054251458:dw

alekos
 one year ago
Best ResponseYou've already chosen the best response.0This will be in metres/min

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433080009777:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0hmm this one is tricky :( Feels like it might be too physics'y for me...

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0it's like a rotational speed that they're asking about, yes? they want to know instantaneous rate of change of some type of ... rotational speed? ugh

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure what variable we're solving for

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is it this? given dz/dt= 10times/min, find dy/dt=? when z=700 ???

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.0hmm i have no idea :( @freckles @amistre64

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@freckles Please help

freckles
 one year ago
Best ResponseYou've already chosen the best response.1the light from the beacon would be the diagonal right?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1I think I want to go ahead and convert your rot/min to rad/min

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{10 rot}{1 \min} \cdot \frac{2\pi rad}{1 rot}=20 \pi \frac{rad}{\min} \\ \]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1himmm... so I guess we will use a trig ratio

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433133523545:dw \[\cos(b)=\frac{z}{300}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1we know db/dt and we are looking for dz/dt

freckles
 one year ago
Best ResponseYou've already chosen the best response.1but in your pic you say we are looking for dy/dt?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1so I guess that means the becan isn't constantly 300m from the runaway

freckles
 one year ago
Best ResponseYou've already chosen the best response.1not sure how to interpret the least distance part

freckles
 one year ago
Best ResponseYou've already chosen the best response.1just because I know @ganeshie8 is awesome I will call him he has great math eyes but I will still try to read this thingy a few more times

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and lol I have my trig ratio thing upside down

freckles
 one year ago
Best ResponseYou've already chosen the best response.1dw:1433135234352:dw I still not entirely sure what to do with the least distance part but I think it is just solving dz/dt from \[\cos(b)=\frac{300}{z}\] I could be wrong though you will have to find sin(b)=opp/hyp so find the opp measurements given those other two measurements haven't you guys been looking at related rates forever now?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1seems like a really big number

unknownunknown
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433135659930:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433136033005:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So z=100sqrt58 and we're trying to find dx/dt?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3lets draw a bit more neat picture

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433136958532:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3we're given frequency, \(f=10 ~\text{revolutions per minute}\) So, \[\dfrac{d\theta}{d t}=\omega =2\pi f = 2\pi (10) = 20\pi~\text{radians per minute} \]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3next suppose you're located at (x, 0) on x axis : dw:1433137645938:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3\[\tan \theta = \dfrac{x}{300}\] differentiate both sides implicitly with respect to \(t\), what do you get ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sec^2\theta(\frac{ d \theta }{ dt })=\frac{ 1 }{ 300 }(\frac{ dx }{ dt })\] Is this correct?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3looks good! i hope you can mange the rest

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I acutally not sure how to go further. hint?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3plugin the value of \(\dfrac{d\theta}{dt}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0(58/9)(20pi)=(1/300)(dx/dt) ??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then I got dx/dt= 348000/9 rad/min ??

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3careful about the units x is not angle, x is the horizontal distance, unit should be "meter"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3it should be : dx/dt= 348000/9 pi meters/min

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oops! Thank you for correcting me! :) and thank you for everything!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And also thank you @freckles! :) Thank you for helping me and trying to solve this question. :)
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