A kite 50ft above the ground moves horizontally at a speed of 4ft/s. How fast is the angle between the string and the horizontal changing when 250ft of string has been let out? (Radians/sec)

Answer 1

Let θ(t) be the angle of inclination at time t and x(t) be this distance of the kite from the starting point at time t.

Make a figure!

When 250 feet of string has been let out θ = arcsin (50/250) = arcsin .2

tan θ(t) = 4t/50

sec²θ dθ/dt = 2/25 and dθ/dt = (2/25)cos²θ