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A-lighthouse-L-is-located-on-a-small-island-2-km-from-the-nearest-point-A-on-a-long-the-straigh-shoreline-If-the-lighthouse-lamp-rotates-at-3-revolutions-per-minute-how-fast-is-the-illuminated-s




Question Number 132225 by bemath last updated on 12/Feb/21
  →A lighthouse L is located on a  small island 2 km from the  nearest point A on a long the  straigh shoreline . If the  lighthouse lamp rotates at 3  revolutions per minute. how fast   is the illuminated spot P on the  shoreline moving along the  shoreline when it is 4 km from A
AlighthouseLislocatedonasmallisland2kmfromthenearestpointAonalongthestraighshoreline.Ifthelighthouselamprotatesat3revolutionsperminute.howfastistheilluminatedspotPontheshorelinemovingalongtheshorelinewhenitis4kmfromA
Answered by mr W last updated on 12/Feb/21
Commented by mr W last updated on 12/Feb/21
x=2 tan θ  (dx/dt)=(dx/dθ)×(dθ/dt)=(2/(cos^2  θ))×(dθ/dt)=2(1+tan^2  θ)×(dθ/dt)  =2[1+((x/2))^2 ]×(dθ/dt)  at x=4:  (dx/dt)=2[1+((4/2))^2 ]×((3×2π)/(60))=π=3.141 km/s
x=2tanθdxdt=dxdθ×dθdt=2cos2θ×dθdt=2(1+tan2θ)×dθdt=2[1+(x2)2]×dθdtatx=4:dxdt=2[1+(42)2]×3×2π60=π=3.141km/s
Commented by bemath last updated on 12/Feb/21
i got (dx/dt) ∣_(x=4 km)  = 60π km/min  sir. correct?  60π ≈ 188.495559 km/min
igotdxdtx=4km=60πkm/minsir.correct?60π188.495559km/min
Commented by mr W last updated on 12/Feb/21
correct!
correct!
Commented by bemath last updated on 12/Feb/21
yes..thanks!
yes..thanks!
Commented by otchereabdullai@gmail.com last updated on 13/Feb/21
nice one prof
niceoneprof

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