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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?

Solution Preview

Attached is a picture of a triangle to show the diagram setup.

Drawing picture is always the first step
in these kind of problems.

let x be the horizontal distance traveled, h be the height, L be the length of string let out and theta be the angle.

Next we need to find that something that is always true about our triangle.

Two things spring to mind:

Pythagoras: x^2 + h^2 = ...

Solution Summary

This shows how to find the rate of change of angle of a flying kite.