Word Problems/Derivatives


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,
y = 20-x
When x = 12 ft:
 the horizontal rate of change is dx/dt = 2 feet per second.
 y = 16 ft

Differentiate y with respect to time.
dy/dt = 0 - dx/dt
2ydy/dt = -2xdx/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.

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Janet Yang


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.


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