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The velocity of an object that leaves the ground is the same as the velocity when it hits the ground on the condition that it is only acted on by gravity, that it lands on an equivalent surface to one that it left in terms of potential energy (altitude]. In a closed system energy must be conserved so an object that leaves the ground with a certain quantity of kinetic energy must hit the ground with the same quantity of kinetic energy as gravity its self which also means that given the surface it lands on is the same in potential energy as the surface it left, the object must have the same velocity as E mv^2/2. Of course the object in real life is subject to friction and various contributing factors so it is only true in an ideal case that the object returns to the ground with the same velocity that it left the ground.

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Q: Object leave ground with same velocity as when it hit ground?
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