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

khi1la2f1qv 2021-11-10 Answered

A boat is pulled into a 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 cons tant rate of 4 feet per second. Determine the speed at which the winch pulls in rope when the re is a tota l of 13 feet of rope out. What happens to the speed at which the winc h pulls in rope as the boat gets closer to the dock ?

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Expert Answer

memomzungup4
Answered 2021-11-11 Author has 14 answers
Let l be the length of the rope. Then l2=144+x2
(a)2ldldt=2xdxdt, so dxdt=lxdldt=lx4=4lx
For l=13,x=5, and dxdt=4135=525ftsec
(b)dldt=xldxdt=5134=2013ftsec
So as L0,dldt increases
Therefore, as the boat gets closer to the dock, its speed increases.
Result: (a)525ftsec, (b)2013ftsec
As the boat gets closer to the dock, its speed increases.

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