Question

Here is the other. Thank you!

A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out?

Answer 1

The angle A = tan^-1 (y/x)
L is the string length
y is the kite height
x = sqrt(L^2 - y^2) = 173.2 ft when L = 200 ft

dA/dt = (dA/dx)*(dx/dt) (y is constant)
dx/dt = 8 ft/s
All you need is the dA/dx derivative, treating y as constant.