The boat will be approaching the dock at ft/min. Note: There is a diagram of thi

Question

The boat will be approaching the dock at ft/min.

Note: There is a diagram of this situation with Problem 30 in Section 3.7 in Anton (8th ed).

A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 10 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 12 ft/min, at what rate will the boat be approaching the dock when 120 ft of rope is out?

The boat will be approaching the dock at ft/min.

Note: There is a diagram of this situation with Problem 30 in Section 3.7 in Anton (8th ed).

Explanation / Answer

Let y =10

ft, the distance the boat is below the pulley.

Let x be the distance from the bottom of the dock to the front of the boat.

Let c be the amount of rope out.

c is the hypotenuse of a right triangle formed between the height of the dock and the distance from the dock t the boat.

y is constant, while x and c are all changing with time, so:

[x(t)]

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