A 9-meter ladder is leaning against the wall of a building, and the base of the ladder is sliding away from the building at a rate of 4 meters per second. How fast is the top of the ladder sliding down the wall when the base of the ladder is 6 meters from the wall?

Answer 1

b^2 + h^2 = 9^2 = 81
2 b db/dt + 2 h dh/dt = 0

at the moment b = 6
h^2 = 81 - 36 = 45
h = sqrt 45 = 6.71
so
2 * 6 * 4 + 2 *6.71 * dh/dt = 0
solve for dh/dt