Question

mount etna erupted on dec. 14 2020 sending lava 104 m into the air. assuming the lava was in free fall, what speed did the lava leave the surface of the volcano at?

Explanation:

Step1: Identify the kinematic - equation

We use the kinematic equation $v^{2}=v_{0}^{2}-2gh$. At the maximum - height, the final velocity $v = 0$. The acceleration due to gravity $g = 9.8\ m/s^{2}$ and the height $h = 104\ m$.

Step2: Solve for the initial velocity $v_{0}$

From $v^{2}=v_{0}^{2}-2gh$, we can re - arrange it to $v_{0}=\sqrt{2gh}$.
Substitute $g = 9.8\ m/s^{2}$ and $h = 104\ m$ into the formula:
$v_{0}=\sqrt{2\times9.8\times104}$
$v_{0}=\sqrt{2038.4}$
$v_{0}\approx45.1\ m/s$

Answer:

$45.1\ m/s$