Falling Ladder !!!
Suppose a ladder that's 10 feet long is (somehow) resting up vertically against a wall.
The bottom of the ladder is then kicked out so that the base of the ladder is moving away from the wall at a rate of 3 ft/sec. (Go ahead and kick the ladder).
At what rate is the ladder's height, h, changing when the bottom of the ladder is 6 feet away from the wall? 9 feet away from the wall?
Use implicit differentiation to determine the answers to these 2 questions, and then check the approximate values of your your results within the applet.
In fact, at any time, you can adjust the values of x and .
1.
Why is the value of always negative (except at x = 0)? Explain.
2.
How far away does the base of the ladder need to be away from the wall in order for ? You can guess-and-check using the applet above. Yet be sure to use calculus to obtain an exact solution!