# Related Rates - Falling Ladder 2

- Author:
- Ms. Orr, Tim Brzezinski

- Topic:
- Calculus, Differential Calculus

Suppose a ladder that's 10 feet long is (somehow) resting up vertically against a wall.
The bottom of the ladder is then kicked out so that the base of the ladder is moving away from the wall at a rate of 3 ft/sec. (Go ahead and

**kick the ladder**).**At what rate is the ladder's height,**when the bottom of the ladder is 6 feet away from the wall? 9 feet away from the wall? Use implicit differentiation to determine the answers to these 2 questions, and then check the approximate values of your your results within the applet. In fact, at any time, you can adjust the values of*h*, changing*x*and .## 1.

**Why is the value of **** always negative** (except at *x* = 0)? Explain.

## 2.

How far away does the base of the ladder need to be away from the wall in order for ? You can guess-and-check using the applet above. Yet be sure to use calculus to obtain an exact solution!