A 13 m ladder leans against a wall. Its foot slides away from the wall at 2 m/s. How fast is its top sliding down when the foot is 5 m from the wall?

Explanation

1. 01

   $x^{2} + y^{2} = 169$; at $x = 5$, $y = 12$. Differentiating, $2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$.

2. 02

   $\frac{dy}{dt} = -\frac{5 \times 2}{12} = -\frac{5}{6}$: the top slides down at $\frac{5}{6}$ m/s.