**A boat is pulled into a dock by means of a winch**

**12 feet above the deck of the boat (see figure).**

**(a) The winch pulls in rope at a rate of 4 feet per second.**

**Determine the speed of the boat when there is 13 feet of**

**rope out. What happens to the speed of the boat as it gets**

**closer to the dock?**

**(b) Suppose the boat is moving at a cons tant rate of 4 feet**

**per second. Determine the speed at which the winch pulls**

**in rope when the re is a tota l of 13 feet of rope out. What**

**happens to the speed at which the winc h pulls in rope as**

**the boat gets closer to the dock ?**

**Answer:**