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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 meter higher than the bow of the boat if the Rope is pulled in at a rate of 1 m/ second how fast is the boat approaching the dock when it is 8 m from the dock so weamp;#39;re trying to find the rate of change of this distance and we know the rate of change of this distance this distance is fixed 1 M so this distance will call X and this distance will call Y we can relate X and Y with the Pythagorean theorem now letamp;#39;s take the derivative of this equation with respect to time using the chain rule we get 2xx dot + 0 is equal to 2 y y dot so solving for x dot okay for X weamp;#39;re going to substitute in 8 m when X is equal to 8 m y is equal to from the Pythagorean theorem and Y dot is going to be -1 m per second because the hypotenuse of this triangle is decreasing in length so the boat is approaching the dock at 1.01 m per second we can omit the negative va