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(D) By the law of conservation of mechanical energy,the total energy at the surface of the earth is equal to the total energy at an infinite distance.

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$\sqrt{2} V_{e}$

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(D) By the law of conservation of mechanical energy,the total energy at the surface of the earth is equal to the total energy at an infinite distance.$K_{i} + U_{i} = K_{f} + U_{f}$Given initial velocity $v_{i} = 2 v_{e}$,where $v_{e} = \sqrt{\frac{2GM}{R_{E}}}$ is the escape velocity.At the surface: $K_{i} = \frac{1}{2} m(2 v_{e})^2 = 2 m v_{e}^2$ and $U_{i} = -\frac{GMm}{R_{E}} = -m v_{e}^2$.At infinity: $U_{f} = 0$ and $K_{f} = \frac{1}{2} m v^2$.Substituting these values:$2 m v_{e}^2 - m v_{e}^2 = \frac{1}{2} m v^2$$m v_{e}^2 = \frac{1}{2} m v^2$$v^2 = 2 v_{e}^2$$v = \sqrt{2} v_{e}$

$A$ particle is projected from the surface of the earth with a velocity equal to twice the escape velocity. When the particle is very far from the earth,its speed would be

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