A 13-foot ladder leans against a wall. The bottom slides away from the wall at 5 ft/s. How fast is the top sliding down when the bottom is 5 feet from the wall?

Core Concept

From $x^2+y^2=13^2$, differentiating gives $2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}=0$. With $x=5$, $y=12$, and $\dfrac{dx}{dt}=5$, this gives $\dfrac{dy}{dt}=-\dfrac{5(5)}{12}=-\dfrac{25}{12}$ ft/s.