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The sun appears to move across the sky, because the earth spins on its axis. To a person standing on the earth, the sun subtends an angle of LaTeX: \theta=9.28\times10^{-3} θ = 9.28 × 10 − 3 rad. How much time (in seconds) does it take for the sun to move a distance equal to its own diameter?

Answer :

Answer:

128 seconds

Step-by-step explanation:

The sun subtends an angle [tex]\theta=9.28\times10^{-3}[/tex] rad

Angular velocity equation is [tex]\omega = \frac{\theta}{t} [/tex]

where [tex]\omega[/tex] is angular velocity and t is time.

Earth spins at a rate of :

[tex]\omega = \frac{2 \pi rad}{24 h \times \frac{3600 s}{1 h}} = 7.27221\times10^{-5}[/tex]  rad/s

Isolating time (t) from angular velocity equation gives:

[tex]\omega = \frac{\theta}{t} [/tex]

[tex]t = \frac{\theta}{\omega} [/tex]

[tex]t = \frac{9.28\times10^{-3}}{7.27221\times10^{-5}}[/tex]

[tex]t = 128 s[/tex]

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