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Problem 30 Medium Difficulty

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?

Answer

decreasing at 0.02 radians per second $\left(\approx 1.15^{\circ} / \mathrm{s}\right)$

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Video Transcript

we know that DX over DT is eight and we want to find dif data over DT because, remember, we want to figure out what rate is the angle between the string and the horizontal decreasing. Therefore, what we know is that data, that's our angle. Is ark sign or signed to the minus one 100 over 200. So you called a pie over sex, which gives us 0.0 point 01 which is the same thing is x over 100 Do too, his negative cassock square data, do you say, huh? Over D. C, which gives us 0.1 times eight because now we can plug in the known values over negative go seek in square times pi over sex which some flies to 0.2 radiance per second. However, if you want this in terms of degrees, this is 1.15 degrees per second