A motorboat starts at the origin and moves in the direction of the positive x-axis, pulling a waterskier along a curve C called a tractrix. See the figure below. The waterskier, initially located on the y-axis at the point (0, a), is pulled by a rope of constant length a that is kept taut throughout the motion. At time t > 0 the waterskier is at point P(x, y). Assume that the rope is always tangent to C. Use the concept of slope to determine a differential equation for the path C of motion.

A motorboat starts at the origin and moves in the direction of the positive x-axis, pulling a waterskier along a curve C called a tractrix. See the figure below. The waterskier, initially located on the y-axis at the point (0, a), is pulled by a rope of constant length a that is kept taut throughout the motion. At time t > 0 the waterskier is at point P(x, y). Assume that the rope is always tangent to C. Use the concept of slope to determine a differential equation for the path C of motion.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section: Chapter Questions

Problem 30RE

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Question

A motorboat starts at the origin and moves in the direction of the positive x-axis, pulling a waterskier along a curve C called a tractrix. See the figure below.

The waterskier, initially located on the y-axis at the point

(0, a),

is pulled by a rope of constant length a that is kept taut throughout the motion. At time

t > 0

the waterskier is at point

P(x, y).

Assume that the rope is always tangent to C. Use the concept of slope to determine a differential equation for the path C of motion.

y′ = ?