SOLUTION: related rates problem:
The spool of a kite is held fixed at 5 feet above the ground. The kite is 105 feet above the ground and traveling eastward in a horizontal fashion. The st
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The spool of a kite is held fixed at 5 feet above the ground. The kite is 105 feet above the ground and traveling eastward in a horizontal fashion. The st
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Question 994013: related rates problem:
The spool of a kite is held fixed at 5 feet above the ground. The kite is 105 feet above the ground and traveling eastward in a horizontal fashion. The string is being let out at 2ft/sec. Find the horizontal speed of the kite when 125 feet of string are let out.
Please explain how to set one of these type problems up. Very confused here.
Thank you
You can put this solution on YOUR website! The spool of a kite is held fixed at 5 feet above the ground. The kite is 105 feet above the ground and traveling eastward in a horizontal fashion. The string is being let out at 2ft/sec. Find the horizontal speed of the kite when 125 feet of string are let out.
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Draw the picture::
You have a right triangle with spool at (0,5), base = h, height = 100,
hypotenuse = string = s
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h^2 = s^2-100^2
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h = sqrt[s^2-100^2)
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dh/ds = (1/2)(s^2-100^2)^(-1/2)*(2s)
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dh/ds = s/sqrt[s^2-100^2)
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h'(125) = 125/sqrt[125^2-100^2] = 125/75 = 5/3 = 1.67 ft/sec
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Cheers,
Stan H.
You can put this solution on YOUR website! I almost agree with stanbon, but is the ratio of increase in horizontal distance to increase in string length.
In other words, the kite travels horizontally per of string released.
Since string is being released at ,
the horizontal speed of the kite (in ft/s) when 125 feet of string are let out is
(