A boy standing at point B on a dock holds a rope of length attached to a boat at point A
Chapter 9, Problem 60(choose chapter or problem)
A boy standing at point B on a dock holds a rope of length attached to a boat at point A [Figure 9(A)]. As the boy walks along the dock, holding the rope taut, the boat moves along a curve called a tractrix (from the Latin tractus, meaning pulled). The segment from a point P on the curve to the x-axis along the tangent line has constant length . Let y = f (x) be the equation of the tractrix. (a) Show that y2 + (y/y ) 2 = 2 and conclude y = y 2 y2 . Why must we choose the negative square root? (b) Prove that the tractrix is the graph of x = ln + 2 y2 y 2 y2 x
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