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 m/s, how fast is the boat approaching the dock when it is 4 m from the dock? Step 1 Using the diagram below, find the relation between x and y. 1 2 72 = x2+1 pulley rope Step 2 We must find dx/dt. Differentiating both sides gives us the following. dy 2y dy = 2x . _ dx dt. dt Step 3 Substituting for dy/dt gives the following. Zy . ( = 2x . - dx it 2y dt dy + 0 dt X