A kite 75ft above the ground moves horizontally at a speed of 2ft/s. At what rate is the angle between the string and the horizontal decreasing when 250ft of string has been let out?

Question

 A kite  above the ground moves horizontally at a speed of  At what rate is the angle between the string and the horizontal decreasing when  of string has been let out?

Answer (in radians per second)

Answer 1

Draw a figure.

Lots of arithmetic needed here, but the "math" is as follows:

Let L be the horizontal distance from the attachment point.

Because the line is assumed parallel to the surface, the angle θ you want to find is such that

tan θ = 75/L i.e.

θ=arctan (75/L

dθ/dt = L²/(75² + L²) (dL/dt)...you know that DL/dt is 2 ft/sec

The only other thing you need is what is L when 250 of line is out. That can be obtained from the Pythagorean Theorem: sqrt(250² - 75²)