Related Rates.
A boat is pulled into a dock by means of a winch 12 ft. above the deck of a boat.
(a) The winch pulls in rope at a rate of 4 ft. per second. Determine the speed of the boat when there is a total of 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 constant rate of 4 ft. per sec. Find the speed at which the winch pulls in rope when there is a total of 13 ft. of rope out. What happens to the speed at which the winch pulls in rope as the boat gets closer to the dock?

I've been stuck on this :/

Question

Related Rates. 
A boat is pulled into a dock by means of a winch 12 ft. above the deck of a boat.
(a) The winch pulls in rope at a rate of 4 ft. per second. Determine the speed of the boat when there is a total of 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 constant rate of 4 ft. per sec. Find the speed at which the winch pulls in rope when there is a total of 13 ft. of rope out. What happens to the speed at which the winch pulls in rope as the boat gets closer to the dock?

I've been stuck on this :/

anonymous · Answer

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anonymous · Answer

thats what it looks like in the diagram given

zarkon · Answer

use the Pythagorean theorem and differentiate implicitly wrt time.

anonymous · Answer

OH thank you. I've got the answer