Question

A ladder 20 feet long leans against a building. If the bottom of the ladder slides away from the building

horizontally at a rate of 2 ft./ sec. How fast is the ladder sliding down the house when the top of the ladder

is 8 feet from the ground?

Answer 1

you have
x^2 + y^2 = 20^2
x dx/dt + y dy/dt = 0
when y=8, x = √(400-64) = 4√21
so now just plug in your numbers:
4√21 * 2 + 8 dy/dt = 0
dy/dt = -√21 ft/s