Which ball lands first: one thrown up or one thrown forward?

If a ball is thrown horizontally, will it still land at the same moment as a ball thrown straight up?

The ball thrown horizontally will land first. Its velocity immediately begins to develop a downward component and it moves downward faster and faster until lands on the ground. In contrast, the ball throw straight up starts with an upward component to its velocity and it rises to a peak height before it begins to develop a downward component to its velocity. Its travel time to the ground is much longer.

A more sophisticated way to look at this question is to recognize that you can separate the horizontal and vertical motions of a falling ball. Since the ball’s weight is purely vertical, it has no effect on the ball’s horizontal motion. The ball’s horizontal motion is that of a coasting: the ball’s horizontal component of velocity never changes. If the ball had any forward component of velocity when you released it, that ball will make steady progress in its forward direction.

The ball’s vertical motion, however, is that of falling: the ball’s vertical component of velocity changes with time as the ball accelerates downward at the acceleration due to gravity. The ball thrown horizontally begins its fall with zero vertical component to its velocity. It’s effectively falling from rest in terms of its vertical motion. It drops faster and faster and soon lands on the ground. The ball thrown upward, however, beings its fall with an upward vertical component to its velocity. It travels upward at first, rising more and more slowly until it reaches its peak height momentarily, and then it descends more and more quickly until it reaches the ground. That second motion, up and then down, takes far longer than the first motion, down only.

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