Answer: [tex]V=10891.39 m/s[/tex]
Explanation:
Since we are told the satellite movs in a circular orbit, we can use the equation of velocity in the case of uniform circular motion:
[tex]V=\sqrt{G\frac{M}{r}}[/tex]
Where:
[tex]V=[/tex] is the velocity of the satellite
[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] is the Gravitational Constant
[tex]M=5.972(10)^{24} kg[/tex] is the mass of the Earth
[tex]r=3360 km \frac{1000 m}{1 km}=3360000 m[/tex] is the radius of the orbit
Solving with the given data:
[tex]V=\sqrt{6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{5.972(10)^{24} kg}{3360000 m}}[/tex]
Finally:
[tex]V=10891.39 m/s[/tex]
