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A spaceship is launched from the Earth's surface with a speed v. The radius of the Earth is R. What will its speed be when it is very far from the Earth? (Use any variable or symbol stated above along with the following as necessary: G for the gravitational constant, m for the mass of the spaceship, and M for the mass of the Earth.)

  • gravity -

    Ke at surface = (1/2) m v^2
    U, potential energy at surface = -G mM/r compared to 0 at infinity
    sum of Ke and U same at surface and infinity
    (1/2)m v^2 -G m M/R = (1/2)m s^2 + 0
    where s is apeed at infinity
    s^2 = v^2 - 2GM/R

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