一道AP微积分题目A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat.If the rope is pulled in at a rate of 1.1 m/s,how fast is the boat approaching the dock when it is 8 m from the dock?只给答案也可以.能写出详细过程就更好了.
问题描述：
一道AP微积分题目
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat.
If the rope is pulled in at a rate of 1.1 m/s,how fast is the boat approaching the dock when it is 8 m from the dock?
只给答案也可以.能写出详细过程就更好了.
答
设船到岸边的距离为x,绳子长度为L
根据勾股定理,x^2+1=L^2
等号两边同时关于t求导
得2x*dx/dt=2L*dL/dt
已知dL/dt=1.1,x=8
可以求出L=sqrt(65)
所以16dx/dt=2sqrt(65)*1.1
解得dx/dt=1.109
错了不要抽我.
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