a student drops a ball from a height of 38.0m. determine all unknowns and answer the following questions…

Explanation:

Step1: Use free - fall displacement formula

The displacement formula for free - fall is $h = v_0t+\frac{1}{2}gt^2$. Since the ball is dropped ($v_0 = 0$), the formula simplifies to $h=\frac{1}{2}gt^2$, where $h = 38.0m$ and $g = 9.8m/s^2$. We can solve for $t$: [t=\sqrt{\frac{2h}{g}}] [t=\sqrt{\frac{2\times38.0}{9.8}}] [t=\sqrt{\frac{76}{9.8}}\approx\sqrt{7.755}\approx 2.78s]

Step2: Use velocity - time formula for free - fall

The velocity - time formula for free - fall is $v = v_0+gt$. Since $v_0 = 0$, then $v = gt$. Substitute $g = 9.8m/s^2$ and $t = 2.78s$ into the formula: [v=9.8\times2.78 = 27.244m/s]

Answer:

How long did the ball remain in the air? 2.78 s What was the ball's speed just before striking the ground? 27.2 m/s