Randall D. Knight — Dynamics I: Motion Along a Line: Problem 35

So-called volcanic “ash” is actually finely pulverized rock blown high into the atmosphere. A typical ash particle is a $50\,\mu\text{m}$-diameter piece of silica with a density of $2400\,\text{kg/m}^3$. a. How long would it take this ash particle to fall from a height of $5.0\,\text{km}$ in vacuum? b. How long in hours does it take this ash particle to fall from a height of $5.0\,\text{km}$ in still air? Use the properties of $20^{\circ}\text{C}$ air at sea level.