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?

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Lindsey Gamble · Accepted Answer

At the moment, dxdt=8 fts and we want to find dθdt. We can find the curren angle first  θ=arcsin⁡100200=π6  Get an equation to relate the x and θ. Differentiate with respect to time t  x100=cot⁡θ  0.01dxdt=csc2θdθdt  dθdt=0.01dxdt−csc2θ  =0.01(8)−csc2π6 plug in known values  =0.08−(2)2  =−0.02 rads  The negative means it is decreasing at 0.02 radians per second (≈1.15∘s)

Chanell Sanborn · Accepted Answer

The angle between the horizontal and the kite θ  Let Height of kite be h  Horizontal distance of kite from where the string is held be x  Then the length of the string be s and will be given by the pythagoras theorem as follows:  s2=h2+x2  Differentiate throughout to get  2sdsdt=2hdhdt+2xdxdt  2sdsdt=2×(0)+2x×8  sdsdt=8x→(1)

A kite 100 ft above the ground moves horizontally at

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