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bri.nguy
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Homework Statement
A balloon is rising vertically from a point on the ground that is 200m from an observer at ground level. The observer determines that the angle of elevation between the observer and the balloon is increasing at a rate of 0.9 degrees/s when the angle of elevation is 45 degrees. How fast is the balloon rising at this time?
Homework Equations
Don't know, other than trig ratios and derivatives.
The Attempt at a Solution
Rate of change of height wrt angle of elevation
h=200tan (thetha)
h'=200sec^2(thetha)
(thetha) = 45
h' = 400 m/degree
400m/degree * .9 degree / s = 360 m/s
Now intuitively this makes no sense because, the difference in height of 45 and 45.9 degrees is about 6m not remotely close to 400...Please help, thanks in advance.