Answer:
 5√3 ft/s
Step-by-step explanation:
Let h represent the horizontal distance of the kite from the person. Let s represent the string length. Then the Pythagorean theorem tells us ...
 s^2 = 100^2 + h^2
 2s·ds/dt = 0 + 2h·dh/dt
 ds/dt = (h/s)·dh/dt
So, we need to know the horizontal distance when s=200.
 200^2 = 100^2 + h^2
 40000 -10000 = h^2
 h = 100√3
Substituting known values into the equation for ds/dt, we have ...
 ds/dt = (100√3)/(200)(10 ft/s) = 5√3 ft/s
The string must be let out at 5√3 ft/s when it is already 200 ft long.
