9. a stone that starts at rest is in free fall for 8.0 s.\na. calculate the stone’s velocity after 8.0…

Explanation:

Step1: Identify the formula for velocity in free - fall

The formula for the final velocity $v$ of an object in free - fall is $v = v_0+gt$, where $v_0$ is the initial velocity, $g$ is the acceleration due to gravity ($g = 9.8\ m/s^2$), and $t$ is the time. The stone starts at rest, so $v_0 = 0\ m/s$. $v=0 + gt$

Step2: Substitute the values of $g$ and $t$

Given $g = 9.8\ m/s^2$ and $t = 8.0\ s$, we substitute these values into the formula. $v=9.8\times8.0$ $v = 78.4\ m/s$

Step3: Identify the formula for displacement in free - fall

The formula for the displacement $y$ of an object in free - fall is $y=v_0t+\frac{1}{2}gt^{2}$. Since $v_0 = 0\ m/s$, the formula simplifies to $y=\frac{1}{2}gt^{2}$. $y=\frac{1}{2}gt^{2}$

Step4: Substitute the values of $g$ and $t$

Given $g = 9.8\ m/s^2$ and $t = 8.0\ s$, we substitute these values into the formula. $y=\frac{1}{2}\times9.8\times8.0^{2}$ $y = 313.6\ m$

Answer:

a. $78.4$ b. $313.6$