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Related Rates - Lighthouse

p269 #34 A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is 1 km from P?
When is the spot of light moving the slowest? Why does the distance d change more quickly or slowly at certain points along the shoreline?