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