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The earth has a radius of 6.38 × 106 m and turns on its axis once every 23.9 h.

(a) What is the tangential speed (in m/s) of a person living in Ecuador, a country that lies on the equator?

(b) At what latitude (i.e., the angle theta in the drawing) is the tangential speed one-third that of a person living in Ecuador?

Respuesta :

lcmendozaf

Answer:

a) V = 465.9 m/s

b) θ = 70.529°

Explanation:

Let's first calculate angular velocity of earth:

[tex]\omega=\frac{2\pi}{23.9h}*1h/3600s[/tex]

Velocity of a person on Ecuador will be:

[tex]V_E = \omega*R[/tex]

[tex]V_E = 465.9 m/s[/tex]

For part b, since angular velocity is the same:

[tex]\frac{\omega*R}{3}=\omega*(R*cos\theta )[/tex]

Solving for θ:

[tex]\theta=acos(1/3)[/tex]

[tex]\theta=70.529\°[/tex]

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