We've all seen this problem, but many of our students haven't.

It's the related rate problem from calculus: the ladder sliding down the wall.

The "official" question?

How fast is the ladder's top sliding down the wall if the bottom is being pulled out at a rate of 1 ft/sec?

We can ask a few questions of kids at any level, though, based on the given that the bottom of the ladder is being pulled to the left at 1 foot per sec.

- Does the top drop at a constant speed?
- Does the top drop a distance equal to the horizontal movement?
- When is the speed of the top greater than 1, less than 1, and equal to 1?
- If this is a 25 foot ladder, with the bottom 7 feet out from the base of the wall, and the top drops 4 feet ... how far out does the bottom of the ladder have to go?

If you want to play with the animation, Ladder Problem. source: @k8nowak

Not related to Calculus, but a personal favourite anyway: what curve describes the midpoint of the ladder (or any other point in the ladder) as the top lands?

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