Question

5.) A 10-foot ladder is placed against a vertical wall such that the bottom of the ladder is

Answer 1

If x is the distance the base of the ladder is from the wall, and y is the distance to top of the ladder is up the wall, then the Pythagorean theorem tells you

... x² + y² = 10²

Differentiating with respect to time, we have

... 2x·dx/dt + 2y·dy/dt = 0

... dy/dt = (-x/y)·dx/dt

We are given x = 6 ft and dx/dt = 3 ft/s. Using the first equation, we can find y as

... y = √(10² -6²) = 8

Then

... dy/dt =(-6/8)·(3 ft/s)

... dy/dt = -2.25 ft/s

The top of the ladder is sliding down the wall at -2.25 ft/s.