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# A rocket is launched straight up from the earth's surface at a speed of 1.80×104 m/s .part awhat is its speed when it is very far away from the earth?

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We can solve the problem using the law of conservation of energy.When the rocket starts its motion from the surface of the Earth, its mechanical energy is the sum of the kinetic energy and gravitational potential energy:wherem is the rocket mass is the rocket's initial velocity is the gravitational constant of the Earth is the mass is the distance of the rocket from the center of the Earth (hence, it corresponds to the radius of the Earth)The mechanical energy of the rocket when it is very far from the Earth is the kinetic energy (due to the gravitational potential in the infinite distance from the Earth is zero):where is the final velocity of the rocket.By equating the initial energy and the final energy, we can find the final velocity: