Two identical balls roll off the edge of a horizontal table top. One leaves traveling at twice the speed of the other. Which ball hits the floor first? Why?

I would say they hit the ground at the same time but im not sure

The balls have different horizontal components of their velocities, but the time of falling down is determined by the time of vertical motion which is identical for both objects t =sqrt(2h/g).

To determine which ball hits the floor first, we need to consider their motion and understand the effect of their initial speed.

When the balls roll off the edge of the table, they experience two types of motion: horizontal motion and vertical motion. The horizontal motion is unaffected by their initial speed, and both balls will have the same horizontal motion.

The vertical motion, however, is influenced by their initial speed. The ball that leaves traveling at twice the speed of the other will have a greater initial vertical velocity. This means it will take longer for gravity to slow down and eventually stop its upward motion.

Now, let's assume that both balls take the same amount of time to reach the ground after falling off the edge of the table. In this case, the ball with the greater initial vertical velocity would have covered a greater vertical distance during that time. Since it has traveled a greater distance, it would have to fall a greater distance to reach the ground. Therefore, it would take longer for the ball with a higher initial speed to hit the floor.

However, we know that both balls start falling at the same time, so the ball with the greater initial speed will take longer to fall to the ground. Hence, the ball that leaves the table traveling at twice the speed of the other will hit the floor later than the slower ball.

what do you think? It does you no value for me to do the thinking first.