Question 994013
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. 
---------------
Draw the picture::
You have a right triangle with spool at (0,5), base = h, height = 100,
hypotenuse = string = s
-----
h^2 = s^2-100^2
----
h = sqrt[s^2-100^2)
-----
dh/ds = (1/2)(s^2-100^2)^(-1/2)*(2s)
-----
dh/ds = s/sqrt[s^2-100^2)
-----
h'(125) = 125/sqrt[125^2-100^2] = 125/75 = 5/3 = 1.67 ft/sec
----------
Cheers,
Stan H.