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Jimmy Perdon

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In summary, the conversation discusses the relationship between the angular position of a bird flying at an altitude of 10m above an observer and its speed when directly above the observer. The equation $\cot{\theta} = \dfrac{x}{10}$ is used to represent this relationship, where $\theta$ is the angle of elevation and $x$ is the horizontal distance. The given information is $\dfrac{d\theta}{dt}$, and the question is to determine $\dfrac{dx}{dt}$ when $\theta = \dfrac{\pi}{2}$.

- #1

Jimmy Perdon

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- #2

skeeter

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have you made a sketch? if so, do you see this relationship?

$\cot{\theta} = \dfrac{x}{10}$

where $\theta$ is the angle of elevation from the observer to the bird, and $x$ is the horizontal distance from the observer to the bird.

you are given $\dfrac{d\theta}{dt}$

differentiate implicitly with respect to time and determine $\dfrac{dx}{dt}$ when $\theta = \dfrac{\pi}{2}$

$\cot{\theta} = \dfrac{x}{10}$

where $\theta$ is the angle of elevation from the observer to the bird, and $x$ is the horizontal distance from the observer to the bird.

you are given $\dfrac{d\theta}{dt}$

differentiate implicitly with respect to time and determine $\dfrac{dx}{dt}$ when $\theta = \dfrac{\pi}{2}$

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- #3

Jimmy Perdon

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Thank you!

The average flying speed of birds at 10m altitude can vary depending on the species, but it is typically between 25-30 miles per hour.

Birds use a combination of flapping their wings and gliding to maintain their speed while flying at 10m altitude. They also adjust the angle of their wings and tail to control their speed.

Yes, birds can fly faster at higher altitudes due to the thinner air and reduced air resistance. Some species, such as migratory birds, take advantage of this to travel long distances more quickly.

Yes, there are several factors that can affect a bird's flying speed at 10m altitude, including wind speed and direction, air temperature, and the bird's physical condition and energy levels.

A bird's body shape and size can greatly impact its flying speed at 10m altitude. Birds with larger wingspans and more streamlined bodies, such as falcons, can reach higher speeds compared to birds with shorter wingspans and bulkier bodies, such as chickens.

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