The object thrown downwards hits the ground first. That should be intuitively obvious.
They both hit the ground at the same speed, however. That follows from conservation of energy.
You and your friend are leaning over the edge of the roof of a tall building. At the same instant you throw a baseball straight up with an initial speed vo and your friend throws a marble straight down with the same initial velocity vo. Assume that you can ignore air resistance. (1) Which object will reach the ground first, the baseball or the marble? (2) How will their speeds compare just before hitting the ground?
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