Answer:
1037 m/s
Explanation:
The linear speed of an object in circular motion is given by:
[tex]v=\omega r[/tex]
where
[tex]\omega[/tex] is the angular velocity
r is the orbital radius
For the Moon, we know that
[tex]r=3.85\cdot 10^8 m[/tex] is the orbital radius
While we know also its orbital period:
[tex]T=27 days \cdot (24\cdot 3600)=2.33\cdot 10^6 s[/tex]
So its angular velocity is
[tex]\omega = \frac{2\pi}{T}=\frac{2\pi}{2.33\cdot 10^6}=2.69\cdot 10^{-6} rad/s[/tex]
And therefore, the linear speed is
[tex]v=\omega r=(2.69\cdot 10^{-6})(3.85\cdot 10^8)=1037 m/s[/tex]