An 8000 kg satellite is launched from the surface of the earth,and injected into outer space a long distance from the earth.The initial velocity needed to launch the satellite into outer space is (G = 6.67 $\times$ 10^-11 Nm²/kg², Me = 5.98 $\times$ 10²⁴ kg, Re = 6.38 $\times$ 10⁶ m) A) 8,450 m/s. B) 9,200 m/s. C) 11,180 m/s. D) 18,900 m/s. E) 25,200 m/s.

Question

Quizplus · Accepted Answer

To launch a satellite into outer space, we need to give it enough kinetic energy to overcome the gravitational attraction of the Earth. The minimum velocity needed to do this is called the escape velocity. The formula for escape velocity is:

Ve = √(2GM/R)

where G is the gravitational constant, M is the mass of the Earth, and R is the distance between the center of the Earth and the center of the satellite (the sum of the radius of the Earth and the distance at which the satellite is launched).

Plugging in the given values, we get:

Ve = √(2 x 6.67 x 10^-11 x 5.98 x 10^24 / (6.38 x 10^6 + 6.38 x 10^6))^0.5 = 11,180 m/s (approx)

Therefore, the best choice is C, 11,180 m/s.

An 8000 Kg Satellite Is Launched from the Surface of the Earth,and