Question

a 16 foot ladder is leaning against a building. the bottom of the ladder os sliding along the pavement at 3 ft/s How fast is the top of the ladder moving down when the foot of the ladder is 2 ft from the wall

Answer 1

Let the distance of the bottom of the ladder from the wall be x, and let the distance of the top of the ladder from the floor be y.
x^2 + y^2 = 256

You want to know dy/dt when dx/dt = 3 and x = 2. At that time, y^2 = 252 and y = 15.87
2x *dx/dt + 2y*dy/dt = 0

dy/dt = -(x/y)*dx/dt = -0.126 dx/dt

Use that equation to calculate dy/dt