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A kite $ 100 ft $ above the ground moves horizontally at a speed of $ 8 ft/s. $ At what rate is the angle between the string and the horizontal decreasing when $ 200 ft $ of string has been let out?

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05:05

Wen Zheng

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Campbell University

Oregon State University

Harvey Mudd College

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

04:33

A kite maintains a constan…

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A girl flying a kite holds…

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A kite string is paid out …

04:17

As a boy winds up the cord…

we know that DX over DT is eight and we want to find dif data over DT because, remember, we want to figure out what rate is the angle between the string and the horizontal decreasing. Therefore, what we know is that data, that's our angle. Is ark sign or signed to the minus one 100 over 200. So you called a pie over sex, which gives us 0.0 point 01 which is the same thing is x over 100 Do too, his negative cassock square data, do you say, huh? Over D. C, which gives us 0.1 times eight because now we can plug in the known values over negative go seek in square times pi over sex which some flies to 0.2 radiance per second. However, if you want this in terms of degrees, this is 1.15 degrees per second

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