Throwing two objects vertically upward

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Maxo
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If one throws an object upward and then a bit later another, is it possible that both objects reach the same maximum height at the same instant of time? When I think about this, I think it must be possible. Why shouldn't it be?
 
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No, the maximum height depends on the initial velocity. If they reach the same maximum height than they must've had the same initial velocity. The two objects' movements are identical but one is a bit delayed so they will NOT reach the top at the same time.