SOLUTION: A kite 100ft above the ground moves horizontally at a speed of 5ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200ft of string h

Question 912080: A kite 100ft above the ground moves horizontally at a speed of 5ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200ft of string have been let out?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A kite 100ft above the ground moves horizontally at a speed of 5ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200ft of string have been let out?
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It's a right triangle.
sin(A) = 100/200 --> A = pi/6
sec^2(A) = 4/3
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x = horizontal distance = sqrt(200^2 - 100^2) = 100sqrt(3)
tan(A) = 100/x
sec^2(A)*(dA/dt) = -1*100/x^2*(dx/dt) = -(100/30000)*5
dA/dt = -(100*(3/4)/(30000))*(5)
dA/dt = -375/30000
= -0.0125 rad/sec

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