related rates: A kite is flying 100 feet above ground at the

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yummymummy1713

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A kite is flying 100 feet above ground at the end of a string 125 feet long. The girl flying the kite lets out the string at the rate of one foot per second. If the kite remains 100 feet above ground, how fast is its horizontal distance from the girl increasing?

Ok, so this makes a pythagorean triangle with dy/dt = 100 ft. Therefore I am able to find dy/dt = 75 ft. So my unknown is dx/dt when y= 100. Do I have to do anything else here? Or is this a trick and I am really done?

~thanks
 
Draw the right triangle formed by the vertical height of the kite above the ground, the horizontal distance along the ground between the girl and the vertical height line, and the "diagonal" length of kite string.

Label the ground distance as x, the height as y = 100 (fixed, so dy/dt = 0), and the string length as s (so ds/dt = 1).

Use the Pythagorean Theorem to create an equation related x, y, and s. Evaluate at y = 100 and s = 125 to find the value of x at the time t in question.

Return to your original equation. Differentiate implicitly with respect to time t. Plug in the known values of x, y, s, dy/dt and ds/dt. Solve for dx/dt.

If you get stuck, please reply showing how far you have gotten in following these steps. Thank you.

Eliz.
 
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