An 8000 kg satellite is launched from the surface of the Earth into outer space. What initial speed is needed by the satellite in order to reach a great (i.e., infinite) distance from the Earth, neglecting the effects of air resistance in the atmosphere? (G = 6.67 × 10⁻¹¹ N·m²/kg², M_E = 5.97 × 10²⁴ kg, R_E = 6.37 × 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

We can use the conservation of energy principle to solve the problem:
Initial energy = Final energy
Initial kinetic energy + Initial potential energy = Final potential energy
1/2 mv^2 - GmM/R = -GmM/∞
where m = 8000 kg, M = 5.97 × 10^24 kg, R = 6.37 × 10^6 m, and ∞ is infinity.
Solving for v, we get:
v = √(2GM/R) = √(2(6.67 × 10^-11)(5.97 × 10^24)/(6.37 × 10^6)) = 11,180 m/s
Therefore, the answer is choice C.

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