Math Arguments

The Ladder Problem

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 right 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?