(Solved): A rope passing through a capstan on a dock is attached to a boat offshore. The rope is pulled in at ...

A rope passing through a capstan on a dock is attached to a boat offshore. The rope is pulled in at a constant rate of 5 ft/s, and the capstan is 6 ft vertically above the water. How fast is the boat traveling when it is 13 ft from the dock? Let x be the horizontal distance from the boat to the dock and z be the length of the rope. Write an equation relating x and z x² +6² = Differentiate both sides of the equation with respect to t (2x) = (22) When the boat is 13 ft from the dock, it is traveling at about (Round to two decimal places as needed) 83% Clear Next