Chapter 3.4, Problem 5E

Unless otherwise stated, in the following problems we assume that the gravitational force is constant with $g=9.81{\text{m/sec}}^{\text{2}}$ in the MKS system and $g=32{\text{ft/sec}}^{\text{2}}$ in the U.S. Customary system.

An object of mass $5\text{ kg}$ is given an initial downward velocity of $50\text{m/sec}$ and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is $-10\text{v}$, where v is the velocity of the object is $\text{m/sec}$. Determine the equation of motion of the object. If the object is initially $500\text{m}$ above the ground, determine when the object will strike the ground.