A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?

Question

A lighthouse is located on a small island 3km away from the nearest point P on a straight shoreline and its light makes 4 revolutions per minute. How fast is the beam of light moving along the shoreline  when it is 1 km from P?

anonymous · Answer

.6 km per minute

anonymous · Answer

hello @TranceNova

anonymous · Answer

$$\tan \theta=y/x$$

anonymous · Answer

$$\sec^2\theta(\frac{ d \theta }{ dt }=\frac{ xdy }{ dt }-\frac{ ydx }{ dt } /(x^2)$$

anonymous · Answer

the right side is all over x^2

anonymous · Answer

$$\frac{ dy }{ dt }=\frac{ x^2(\sec^2\theta)\frac{ d \theta }{ dt } +y\frac{ dx }{ dt }}{ x }$$

trancenova · Answer

yep yep

anonymous · Answer

$$\frac{ 3^2(\frac{ 1 }{ \cos^2\theta })(8\pi)+1(0) }{ 3 }$$

anonymous · Answer

|dw:1348714601605:dw|

anonymous · Answer

@TranceNova my question to you is, whats the answer for 1/cos^2o?

anonymous · Answer

my book says the answer is 8pi/3 km/min but isnt cos^2theta  (3/root10)^2?

anonymous · Answer

@bahrom7893 hey

anonymous · Answer

so im pretty much at the end, and I want to now what i am messing up :) thanks for listening

bahrom7893 · Answer

Wait I'm kinda lost.. let me reread the problem.

bahrom7893 · Answer

im getting 80pi/3

anonymous · Answer

so it is 10 right?

bahrom7893 · Answer

http://answers.yahoo.com/question/index?qid=20110308160630AAZ3vZc This answer summarizes it nicely

anonymous · Answer

ok good, thank you so much @bahrom7893 !