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An airplane flying horizontally at a constant height of 1000 m above a fixed radar station. At a certain instant the angle of elevation θ at the station is π 4 radians and decreasing at a rate of 0.1 rad/sec. What is the speed of the aircraft at this moment?

Respuesta :

davidlcastiblanco

Answer:

[tex]v=200m/s[/tex]

Explanation:

To determine the speed of the aircraft the image illustrate better the situation

So

[tex]v=\frac{x}{t}[/tex]

As the image determine the x distance can be also find as a

[tex]x=H*cot(\alpha)[/tex]

[tex]H=1000m[/tex]

[tex]v=\frac{dx}{dt}[/tex]

Using geometry concepts in angles

[tex]v=1000*\frac{-1}{(sin\alpha)^2}*\frac{d\alpha}{dt}[/tex]

[tex]v=1000*\frac{-1}{\frac{1}{\sqrt{2}}}*-0.1rad/s[/tex]

[tex]v=1000m*\frac{-1}{0.5}*-0.1[/tex]

[tex]v=1000m*0.2rad/s[/tex]

[tex]v=200m/s[/tex]

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