You are here:

- Home
- Science
- Math for Kids
- Word Problems
- Derivatives

Advertisement

What is the answer to this word problem? Trigonometry can be used to assist in getting the answer, but derivatives or differentiation must be used.

A 20 foot ladder is leaning against a house when its base starts to slide away. By the time the base is 12 feet from the house, the base is moving at 2 feet/second? How fast is the ladder sliding down the wall at that moment?

By the Pythagorean Theorem,

y² = 20²-x²

When x = 12 ft:

the horizontal rate of change is dx/dt = 2 feet per second.

y = 16 ft

Differentiate y² with respect to time.

dy²/dt = 0 - dx²/dt

2y·dy/dt = -2x·dx/dt

dy/dt = (-x/y)·dx/dt

x=12, y=16, dx/dt=2 ft/sec:

dy/dx = (-12/16)·2 = -1.5

The ladder slides down the wall at 1.5 feet per second.

- Add to this Answer
- Ask a Question

Rating(1-10) | Knowledgeability = 10 | Clarity of Response = 10 | Politeness = 10 |

Comment | Perfect, just perfect! |

Word Problems

Answers by Expert:

Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.
**Publications**

Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.**Education/Credentials**

I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley,
and a Master of Business Administration degree from The Wharton School.**Past/Present Clients**

George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.