Answer to Question #320388 in Calculus for Banoy

Question

a ladder 20 feet long leans against a vertical building is the tower of the ladder slides down at a rate of p3 fits how fast is the bottom of the ladder sliding away from the building in the top of the ladder is 10 feet above the ground

Answer 1

$y-height\,\,above\,\,the\,\,ground\\x-dis\tan ce\,\,of\,\,the\,\,bottom\,\,to\,\,the\,\,wall\\x=\sqrt{20^2-y^2}\\\frac{dy}{dt}=-3\\\frac{dx}{dt}=\frac{1}{2\sqrt{20^2-y^2}}\cdot \left( -2y \right) \frac{dy}{dt}=-\frac{y}{\sqrt{400-y^2}}\cdot \left( -3 \right) =\\=\frac{3\cdot 10}{\sqrt{400-10^2}}=1.73205\,\,$