A ladder 10 feet long is resting against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 1 foot per second, how fast is the top of the ladder moving down when the bottom of the ladder is 8 feet from the wall?
The picture looks like this.
We have dx/dt = 1 ft/sec, and we want dy/dt.
x and y are related by the Pythagorean Theorem
Differentiate both sides of this equation with respect to t to get
When x = 8 ft, we have
The top of the ladder is sliding down (because of the negative sign in the result) at a rate of 4/3 feet per second.