Posted by **fati** on Saturday, June 16, 2012 at 2:09am.

The beacon on a lighthouse makes one revolution every 20 seconds. The beacon is 300 feet from

the nearest point, P, on a straight shoreline. Find the rate at which the ray of light moves along

the shore at a point 200 feet from P.

- calculus -
**Reiny**, Saturday, June 16, 2012 at 9:29am
Make a sketch, let the distance between the end of the ray of light and point P be x ft

let the angle formed at that moment be Ø

then,

tanØ = x/300

x = 300tanØ

dx/dt =300sec^2 Ø dØ/dt

let the hypotenuse be h

when x=200

h^2 = 200^2+300^2

h = 100√13

secØ = 100√13/300 = √13/3

sec^2 Ø = 13/9

and we are told dØ/dt = 2π/20 rad/sec

= π/10 rad/sec

dx/dt = 300(13/9)(π/10) = 130π/3 ft/sec

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