[Physics] Which ball will hit the ground first?A ball simply dropped or a ball thrown across the room

kinematicsnewtonian-mechanicsprojectile

I've read that gravity doesn't affect an object's horizontal motion or vice versa, and some people told me that both balls will reach the ground at the same time. How is this possible, isn't that when a ball is thrown its resultant force changes (using basic vector, gravity and its horizontal force), thus causing a change in acceleration? But how is it possible that the ball reaches the ground at the same time?

Best Answer

Let's say that you throw the first ball with a horizontal velocity component $v_x$ and vertical component of $0$. The other ball is simply dropped.

What happens if you start running at $v_x$ in the same direction as the thrown ball instantaneously after you release it? It appears to have no horizontal velocity, and just falls downwards, accelerating from a vertical velocity of $0$. Its motion appears identical to that of the dropped ball to a stationary observer: it appears to reach the ground at the same time, though you aren't messing with it in any way.