Flying a kite . A girl flies a kite at a height of 3000 ft, the wind carrying the kite horizontally away from her at a rate of 25 ft/sec. How fast must she let out the string when the kite is 500 ft away from her ?

Explanation

Let K be the kite and G be the girl. Let PK=x
`:. " " (300)^(2)+x^(2)=l^(2)`
` :. " " 2x(dx)/(dt)=2l(dl)/(dt)`
`:. " " (dl)/(dt)=(x)/(l)(dx)/(dt)=25 cos theta`
Speed of end along rope `=25 cos theta =25 xx(4)/(5)=20 ft//s`
(`:. cos theta =(4)/(5) "when" l=500`)