1) Allison's angular velocity: 0.262 rad/h
2) Allison's linear velocity: 837.6 mi/h
Step-by-step explanation:
1)
The angular velocity of a body is the rate of change of the angular position. Mathematically:
[tex]\omega=\frac{\Delta \theta}{\Delta t}[/tex]
where
[tex]\Delta \theta[/tex] is the angular displacement
[tex]\Delta t[/tex] is the time taken
Allison makes one complete revolution around the Earth's axis in 1 day (24 hours), so
[tex]\Delta t = 24 h[/tex]
The angular displacement instead is
[tex]\Delta \theta=2\pi rad[/tex]
which corresponds to the angle of one complete revolution. Therefore, Allison's angular velocity is
[tex]\omega=\frac{2\pi}{24}=0.262 rad/h[/tex]
2)
The linear velocity of a body in circular motion is given by
[tex]v=\omega r[/tex]
where
[tex]\omega[/tex] is the angular velocity
r is the distance from the axis of rotation
For Allison, we have
[tex]\omega=0.262 rad/h[/tex]
Now we have to find r, the distance of Allison from the Earth's axis.
We know that her latitude is
36.1627° N
Which is the angle between the Earth's radius and the equator, and the Earth radius is
R = 3960 miles
Therefore, Allison's distance from the Earth's axis can be found using trigonometry:
[tex]r=R cos \theta = (3960)cos(36.1627^{\circ})=3197 mi[/tex]
And so, Allison's linear velocity is:
[tex]v=(0.262)(3197)=837.6 mi/h[/tex]
Learn more about rotational motion:
brainly.com/question/9575487
brainly.com/question/9329700
brainly.com/question/2506028
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