ball rolls with a speed of 2 m/s across tabletop that is 1 meter above floor. Reaching edge of table, ball follows parabolic path to landing spot on floor. How far along the flor is this spot from the table?

How do I set this up? Thank you.

To set up this problem, we need to consider the motion of the ball when it rolls off the edge of the table. Here's the step-by-step process to solve the problem:

1. Start by analyzing the initial horizontal motion of the ball, which is rolling with a speed of 2 m/s across the tabletop. Since there are no external horizontal forces acting on the ball, it will continue to move horizontally at a constant speed.

2. The ball's initial vertical velocity as it leaves the table is 0 m/s because it rolls off without any vertical force acting on it. However, it will experience the force of gravity during its vertical motion.

3. Next, we need to find the time it takes for the ball to reach the ground. We can use the fact that the vertical motion of the ball follows a parabolic path under the influence of gravity. The vertical motion can be described using the kinematic equation: h = ut + (1/2)gt^2, where h is the height, u is the initial velocity, g is the acceleration due to gravity, and t is the time.

In this case, the height is 1 meter (the distance between the tabletop and the floor), the initial velocity (u) is 0 m/s, and the acceleration due to gravity (g) is approximately 9.8 m/s^2. By plugging these values into the equation, we can solve for the time it takes the ball to reach the ground.

4. Once we have the time it takes for the ball to reach the ground, we can use it to calculate the horizontal distance it traveled during that time. Since the horizontal motion is uniform and the ball moves at a constant speed of 2 m/s, we can use the equation: distance = speed * time.

Plug in the value of the speed (2 m/s) and the time (which we found in the previous step) to calculate the horizontal distance traveled by the ball.

By following these steps, you should be able to set up and solve the problem to find the horizontal distance along the floor where the ball lands.