A boy standing at comer A of a rectangular pool has a boat in comer B on the end

Question

A boy standing at comer A of a rectangular pool has a boat in comer B on the end of a string that is 30 feet long. He walks along the side of the pool toward C, keeping the string taunt. Find an equation of the boat's path. That is, find a relationship between x and y. Hints: Consider the right triangle with hypotenuse PE. Note that the tangent of theta can be expressed in terms of the side lengths of this triangle and that dy/dx = tan theta. You might also find that it is easier to solve this DE for x than for y. You may use a CAS to do the integration. What is the distance from AB to the boat when the boat is half way across the pool? How far has the boy walked at that time?

Explanation / Answer

tan() =y/x

1. sqrt(x^2+y^2)= 30

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