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Physics
18.06.2022 22:18
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You are standing on the ground, watching a bird fly away horizontally at a rate

You are standing on the ground, watching a bird fly away horizontally at a rate of 9 meters per second. the bird is initially located 25 meters above your head. let θ be the angle measured from the vertical direction to the direction from you to the bird. how fast (in radians per second) is θ changing when the horizontal distance between you and the bird is 12 meters
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jaylaa04
jaylaa04
4,5(69 marks)

\dfrac{d\theta}{dt}= 0.293\ rad/s

Explanation:

horizontal distance traveled by the bird is equal to be x

given,

height of the bird above his head = 25 m

angle between them is equal to θ

\dfrac{dx}{dt} = 9 m/s

d² = x² + y²

\theta = tan^{-1}{\dfrac{x}{25}}

\dfrac{d\theta}{dx}= \dfrac{1}{1+(\dfrac{x}{25})^2}\times(\dfrac{1}{25})

\dfrac{d\theta}{dx}= \dfrac{25}{x^2+625}

now,

\dfrac{d\theta}{dt}= \dfrac{d\theta}{dx}\times \dfrac{dx}{dt}

\dfrac{d\theta}{dt}= \dfrac{25}{x^2+625}\times 9

\dfrac{d\theta}{dt}= \dfrac{225}{x^2+625}

at x = 12 m

\dfrac{d\theta}{dt}= \dfrac{225}{12^2+625}

\dfrac{d\theta}{dt}= 0.293\ rad/s

darkremnant14
darkremnant14
4,5(69 marks)

Radiation

Explanation:

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