Calculus Question

Question

A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 5 feet below the level of the pulley.



If the rope is pulled through the pulley at a rate of 18 ft/min, at what rate will the boat be approaching the dock when 100 ft of rope is out?

Answer 1

x² + 5² = l²; 2xdx/dt = 2ldl/dt; dx/dt = (l/x)dl/dt = 100/√(100² - 25)·18ft/min = 18.0225 ft/min