Answer: [tex]= 0.013 rads^{-1}[/tex]
Step-by-step explanation:
given data:
speed of kite = 5 ft/s
height of the kite = 100 ft above the ground.
decrease = 200 ft
Solution:
[tex]\frac{dy}{dx} = 5 ft/s\\\\\\[/tex]
θ = [tex]arcsin \frac{100}{200}[/tex]
next we relate θ and x with respect to time t.
[tex]\frac{x}{100} =[/tex] cot θ
[tex]0.01\frac{dx}{dt} =-csc^{2}[/tex] θ[tex]\frac{d}{dt}[/tex]
[tex]\frac{d}{dt} = \frac{0.01\frac{dx}{dt} }{-csc^{2} \frac{\pi }{6} }[/tex]
[tex]= \frac{0.01(5)}{-csc^{2}\frac{\pi}{6} }[/tex]
[tex]= \frac{0.05}{-2^{2} }[/tex]
[tex]= 0.013 rads^{-1}[/tex]
