Answer:
3.1 ft/sec
Explanation:
we are talking about a right-angled triangle.
the Hypotenuse c is the line (rope) connecting the boat and the winch.
the side a is the height of the winch (8 ft straight up from the water level).
the side b is the distance of the boat to the dock on the surface of the water. 6ft.
c² = 8² + 6² = 100
c = 10 ft
when pulling in 1.5 ft of the rope, I create a new triangle, where side a is still the same, the new side c is 1.5 ft shorter than the original one, and we need to calculate the new side b based on that.
the difference of original b and new b is then the distance per second (= the rate) of the boat being pulled at that point.
so,
(10-1.5)² = 8² + b²
8.5² = 64 + b²
72.25 = 64 + b²
8.25 = b²
b = 2.9 ft
original b - new b = 6 - 2.9 = 3.1 ft
=> the boat's rate is 3.1ft/sec
