(Solved): 6. An object of mass m is falling from the height h above a surface with velocity v0 under the i ...

6. An object of mass $m$ is falling from the height $h$ above a surface with velocity $v_0$ under the influence of gravity $g$ with air resistance proportional to its velocity. If $y(t)$ denotes the distance fall at time $t$ in which the downward direction is assume to be positive, then the motion of the objects satisfies the differential equation $m\frac{d^{2}y}{d{t}^2}+k\frac{dy}{dt}=mg$ Solve this equation with initial condition $y=0$ and $y^{?}=v_0$ when $t=0$.