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Falling Ladder

Related Rates - Falling Ladder

A ladder is leaning against a wall when the base begins to slide at a constant rate.

1. Click "reset time" and "slide ladder". At what rate is the base of the ladder sliding away from the wall?

2. Why isn't the third side labeled with a variable like the red and blue sides?

3. Is the top of the ladder falling towards the ground at a constant rate, increasing rate, or decreasing rate? How do you know?

4. Drag the red point labeled "move time" until the base of the ladder is 20 feet from the wall. It will take exactly 2.5 seconds for the ladder to fall the rest of the way to the ground. Briefly exlain. What will the average velocity be for the top of the ladder during this 2.5 seconds? How about the bottom?

5. Drag the red point labeled "move time" until the speed of the top of the ladder is one fourth the speed of the bottom of the ladder. How do the lengths of the red & blue line compare at that time?

6. Would there be a maximum speed at which the top of the ladder is sliding towards the floor if the ladder were to continue all the way to the floor? Give the maximum speed or explain why there isn't one.