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Related Rates... change in angle formula...

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Date Posted: 10/23/2006 1:37:26 AM  Status: Live
Related Rates... change in angle formula...
Course Textbook Chapter Problem
Calculus Calculus (5th) by Stewart 3.9 24
Question Details:
No idea how to do this at all...
A kite 100 ft above the ground moves horizontally at a speed of 8ft/s.  at what rate is the angle between the string and the horizontal decreasing when 200 ft of string have been let out?

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Oracle
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Date Posted: 10/23/2006 3:28:48 AM  Status: Live
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Response:

We need to find a couple of relations for this problem.
First,    and
Take the derivative of each to find the formulas for rates of change.
   and  
Using the first equation, when h=200 ft, x=173.2 ft, y=100 ft,  θ=60 degrees,
dx/dt=8 ft/sec  dy/dt=0 ft/sec  dh/dt=6.928 ft/sec

Now using the second equation dθ/dt=-.03464 degrees/second 

 

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