Question

a student drops a ball from a height of 38.0m. determine all unknowns and answer the following questions. neglect drag. how long did the ball remain in the air? what was the balls speed just before striking the ground?

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