9. a ball is rolled across a level laboratory table and allowed to roll off the table and strike the floor…

Explanation:

Step1: Identify the vertical - motion equation

The vertical - motion of the ball is a free - fall motion. The equation for the vertical displacement $y$ of an object in free - fall is $y = v_{0y}t+\frac{1}{2}gt^{2}$, where $v_{0y}$ is the initial vertical velocity, $t$ is the time of fall, and $g$ is the acceleration due to gravity ($g = 9.8\ m/s^{2}$). When the ball rolls off the table, the initial vertical velocity $v_{0y}=0\ m/s$.

Step2: Simplify the equation

Since $v_{0y} = 0\ m/s$, the equation simplifies to $y=\frac{1}{2}gt^{2}$.

Step3: Substitute the values

We know that $t = 0.391\ s$ and $g = 9.8\ m/s^{2}$. Substitute these values into the equation: $y=\frac{1}{2}\times9.8\times(0.391)^{2}$. First, calculate $(0.391)^{2}=0.152881$. Then, $\frac{1}{2}\times9.8\times0.152881 = 4.9\times0.152881=0.7491169\approx0.75\ m$.

Answer:

0.75 meter