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?

Answer 1

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