Question

a student drops a ball from a height of 49.0m. 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: Find time in air

Use the equation $h = v_0t+\frac{1}{2}gt^2$. Since the ball is dropped, $v_0 = 0$. The equation simplifies to $h=\frac{1}{2}gt^2$. Solving for $t$, we get $t=\sqrt{\frac{2h}{g}}$. Given $h = 49.0m$ and $g = 9.8m/s^2$.
$t=\sqrt{\frac{2\times49.0}{9.8}}$

Step2: Calculate time value

$t=\sqrt{10}\approx 3.16s$

Step3: Find speed before hitting ground

Use the equation $v = v_0+gt$. Since $v_0 = 0$, $v = gt$. Substitute $g = 9.8m/s^2$ and $t = 3.16s$.
$v=9.8\times3.16$

Step4: Calculate speed value

$v\approx31.0m/s$

Answer:

How long did the ball remain in the air? 3.16 s
What was the ball's speed just before striking the ground? 31.0 m/s