A 13-m ladder leans against a wall. Its top slides down at 0.5 m/s. When the foot is 5 m from the wall, the foot is moving at:

$x^2 + y^2 = 169$. At foot = 5: $y = 12$. Differentiate: $2x \dot x + 2y \dot y = 0$ ⇒ $\dot x = -y\dot y/x = -12(-0.5)/5 = 1.2$ m/s.