Question

a baseball and a bowling ball roll off a table at the same time. which one reaches the ground first? (1 point)
the baseball hits first
the bowling ball hits first
they both hit at the same time
not enough info given

Explanation:

Step1: Analyze vertical - motion

Both balls are in free - fall motion vertically. The initial vertical velocity \(v_{0y}=0\ m/s\), and the acceleration due to gravity \(g\) is the same for both (\(g = 9.8\ m/s^{2}\) near the Earth's surface). The vertical displacement \(y - y_{0}\) is the height of the table.
The equation for vertical displacement in free - fall is \(y - y_{0}=v_{0y}t+\frac{1}{2}gt^{2}\). Since \(v_{0y} = 0\), it simplifies to \(y - y_{0}=\frac{1}{2}gt^{2}\), and \(t=\sqrt{\frac{2(y - y_{0})}{g}}\).

Step2: Determine time of fall

The time of fall \(t\) depends only on the height of the table (\(y - y_{0}\)) and the acceleration due to gravity \(g\), and not on the mass or horizontal motion of the balls. Since they start from the same height, they will take the same time to reach the ground.

Answer:

They both hit at the same time