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Newton's second law, the law of universal gravitation and the centripetal acceleration allows to find the correct answer for the question about the speed of the satellite is:
c) The speed of satellite is: 7287 m/s
Law of Universal Gravitation and Newton's Second Law.
Newton's second law states that the force on a body is proportional to the product of the mass times the acceleration of the body and the attraction between the bodies is expressed in the law of universal gravitation
F= ma
F =[tex]G \frac{Mm}{r^2}[/tex]
Where f is the force, m and M the mass of each body, the acceleration and r the distance between them.
Let's substitute.
[tex]a= G \frac{M}{r^2}[/tex]
The centripetal acceleration is the acceleration towards the center of the movement, it is given by the relation.
[tex]a = \frac{v^2}{r}[/tex]
Where a is the acceleration, v is the tangential speed and r the radius of the circle
Let's substitute.
[tex]G \frac{M}{r^2} = \frac{v^2}{r} \\v= \sqrt{\frac{GM}{r} }[/tex]
indicate that the radius of the orbit is r= 7500000m = 7.5 10⁶ m
Let's calculate.
[tex]v= \sqrt{\frac{6.67 \ 10^{-11} \ 5.97 \ 10^{24 }} { 7.5 \ 10^6 } } \\v= \sqrt{53.093 \ 10^6}[/tex]
v= 7,287 10³ m/s
When reviewing the answers, the correct result is:
c) the speed is: 7287 m/s
In conclusion using Newton's second law, the law of universal gravitation and the centripetal acceleration we can find the correct result for the question about the speed of the satellite is:
c) the speed is: 7287 m/s
Learn more about the law of universal gravitation and centripetal acceleration here: brainly.com/question/14113448
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