Throwing two objects vertically upward

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When two objects are thrown vertically upward at different times, they cannot reach the same maximum height simultaneously. The maximum height achieved by each object is determined by its initial velocity. If both objects reach the same height, they must have the same initial velocity, which contradicts the timing of the throws. Therefore, despite potential similarities in height, the delayed throw ensures that the objects will not peak at the same moment. The physics of motion dictates that their ascent times will differ.
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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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Are you throwing them from the same height?
 
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.
 

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