A 20 ft. ladder is leaning against a house while the base is pulled away at a constant rate of 1 ft/s. At what rate is the top of the ladder sliding down the side of the house when the base is:

1. $\quad 1$ foot from the house? ft/s
2. $\quad 5$ feet from the house? ft/s
3. $\quad19$ feet from the house? ft/s

Warning: Take care with plus/minus signs. This problem asks for velocity in the downward direction. Velocity downward and velocity upward have opposite signs because up and down point in opposite directions!