A relative rates calculus problem regarding a kite.

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

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/calculus-and-analysis/a-relative-rates-calculus-problem-regarding-a-kite-1n7

Solution Preview

...

Trig:
sin(theta) = h/L
cos(theta) = x/L
tan(theta) = h/x

We want x in the equation and h is constant so I would lean towards the
last one. It will be easier if we take the reciprocal and get the cotangent.
cot(theta) = x/h

Being calculus, we have to take the derivative with respect to time:

-(1/sin^2(theta)) theta' = x'/h

using chain rule because theta depends on ...