Does velocity affect the kinetic energy of falling objects?

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mohabitar
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Three identical balls are thrown from the edge of a cliff, each with the same initial speed. Ball 1 is thrown directly upward. Ball 2 is thrown directly downward. Ball 3 is thrown horizontally. Which of the following statements correctly characterizes the relative kinetic energies (K) of the three balls just before hitting the ground.

The correct answer for this is that theyre all equal, but that doesn't make sense to me. If the first ball is thrown directly upward, then when its done climbing the top, it will have more time to accelerate downward than all the other balls. The more time it has to accelerate, the faster it's velocity will become, and KE=1/2MV^2, so the larger the velocity, the larger the KE. And ball 2 and 3 having the same KE makes sense, but I figured ball 1 should be greater. Where did I go wrong?
 
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Determine the velocity when the first ball, falling down from the top height, reaches the edge of the cliff again. You will see that it is equal in magnitude as the initial velocity was. From here, it moves as ball 2. ehild