Question

A ladder 25 feet long is leaning against a house. The base of the ladder is pulled away from the wall at a rate of 2 ft/sec. How fast is the top moving down the wall when the base of the ladder is 15 feet from the wall?

Answer 1

W = distance from wall H = height of wall to ladder

W^2 + H^2 = 25^2 Pythagorean theorem

2 W dW/dt = -2 H dH/dt differentiating

dH/dt = -W / H * dW/dt

15^2 + H^2 = 625 when base of ladder is 15 ft from wall

H^2 = 400 H = 20 height of ladder on wall

dH/dt = -15 / 20 * dW/dt = -3/4 dW/dt

dH/dt = -3/4 * 2 = -1.5 ft/sec