Question

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 1

Answer:

128 seconds

Step-by-step explanation:

The sun subtends an angle $\theta=9.28\times10^{-3}$ rad

Angular velocity equation is $\omega = \frac{\theta}{t}$

where $\omega$ is angular velocity and t is time.

Earth spins at a rate of :

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

Isolating time (t) from angular velocity equation gives:

$\omega = \frac{\theta}{t}$

$t = \frac{\theta}{\omega}$

$t = \frac{9.28\times10^{-3}}{7.27221\times10^{-5}}$

$t = 128 s$