A boat is pulled into a dock by a rope with one end attached to the front of the boat and the other end passing through a ring attached to the dock at a point 5 feet higher than the front of the boat. The rope is being pulled through the ring at the rate of 0.6 ft/sec. How fast is the boat approaching the dock when 13 feet of rope are out

The boat is approaching the dock  at 0.65 ft/sec when 13 feet of rope are out.

Step-by-step explanation:

Let x be the length of rope and y be the distance between boat and dock.

Height of point where a ring attached =z=5 feet

x=13 feet

Using Pythagoras theorem

Differentiate w.r.t t

Hence,the boat is approaching the dock  at 0.65 ft/sec when 13 feet of rope are out.