Question

A child is flying a kite. If the kite is 125 feet above the child's hand level and the wind is blowing it on a horizontal course at 7 feet per second, the child is letting out cord at _____ feet per second when 245 feet of cord are out. Assume that the cord remains straight from hand to kite.

Answer 1

Kite string angle relative to horizontal = sin^-1(125/245) = 30.7 degrees.

String horizontal location = x
dx/dt = 7 ft/s
L = sqrt (x^2 + y^2)
(y is constant at 125 ft)

You want dL/dt = (dL/dx)*(dx/dt)
dL/dx = x/sqrt(x^2 + y^2)]

Take it from there.