Asked by Sarah
A lighthouse 2 miles offshore has a light that rotates once every 20 seconds. At what rate is the light traveling along the shore if it is shining on a point 4 miles along the shore from the point nearest the lighthouse?
Answers
Answered by
Steve
Draw a diagram. It is clear that when the distance of the beam from the point P on shore nearest the lighthouse is x,
tanθ = x/2
sec^2θ dθ/dt = 1/2 dx/dt
when x=4, we have
(1+(4/2)^2)(2π/20) = 1/2 dx/dt
dx/dt = π mi/s
tanθ = x/2
sec^2θ dθ/dt = 1/2 dx/dt
when x=4, we have
(1+(4/2)^2)(2π/20) = 1/2 dx/dt
dx/dt = π mi/s
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