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Math Help - Related Rates word problem: Boating

  1. #1
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    Related Rates word problem: Boating

    A boat is pulled into dock by means of a winch 12 feet above the deck of the boat.

    a) The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 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 feet per second. Determine the speed at which the winch pulls in rope when there is a total of 13 feet of rope out. What happens to the speed at which the winch pulls in rope as the boat gets closer to the dock?
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  2. #2
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    Re: Related Rates word problem: Boating

    For part a), sketch a right triangle height = 12 ft, hypotenuse = 13 ft. boat speed is horizontal. The speed component along the rope is 4 ft/s. What is the horizontal speed component of the boat? You do not know the angle between the rope and the horizontal, but you can work around it. The second part of the question, is qualitative analysis, what happens to the angle between the horizontal and the rope. Make the connection with the velocity change, does it increase or decrease, justify your conclusion.

    Complete part a). If you still need help in part b) repost the question.
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