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## Homework Statement

In a lighthouse that is 2km from the shore, the searchlight rotates clockwise once every 50s. How fast is the spot of light on the shore moving: a) When it's directly opposite the island? b) When it is 1km from the point opposite the island?

## Homework Equations

implicit differentation

## The Attempt at a Solution

I started with a right triangle diagram, where the right angle is the point opposite the lighthouse (I included a diagram to show what I drew). My problem seems to be incorporating the time of rotation into the question. I can easily get an equation by using Pythagorean's Theorem, but I don't know how time would be used in this equation. Any help would be appreciated, thanks in advance.