Question

A boat is pulled into a dock by means of a rope attached to a pulley on the dock (see the accompanying figure). The rope is attached to the bow of the boat at a point 12 ft below the pulley. How fast must the rope be pulled if we want the boat to approach the dock at a rate of 8 ft/min at the instant when 105 ft of rope is out? Round your answer to two decimal places.

Answer 1

Firstly, we will draw diagram

we are given

we can use Pythagoras theorem

we can solve for x

we can find derivative with respect to t

now, we can plug values

..........Answer