Related Rates - The Sliding Ladder
- Ken Schwartz
The topic of "Related Rates" helps us to understand how one rate of change is related to another. The "Sliding Ladder" problem is a classic example. A ladder rests upright against a wall. Suddenly, the bottom of the ladder begins to slide away from the wall at a constant rate. (Imagine a cockroach is pushing it). How fast is the top of the ladder sliding down the wall at any given distance of the bottom from the wall?
If the ladder is not upright against the wall, click the Reset button. Then click the Start/Stop button to start the ladder sliding. One this run, watch the bottom of the ladder to convince yourself that it is moving at a steady rate. Reset and restart the animation, this time watching the top of the ladder against the wall. Notice how, while the bottom of the ladder moves steadily, that the top moves downward faster and faster. The speed is graphed and displayed numerically as the ladder slides.