The first order linear differential equation
mv' + bv = mg
is a simplified description of the motion (velocity) of an object of mass m dropping vertically under constant gravitational acceleration g and linear air resistance (viscous friction) -bv. Assuming the object begins its motion from rest, and at an initial height h from the surface of the earth:

a) Calculate the velocity of the object as a function of time using the Laplace transform approach.
b) Does the object reach a terminal velocity? If so, what is this terminal velocity? Note that the terminal velocity is the (constant) velocity reached after a sufficiently large time.
c) Compare the solution obtained for velocity in a) with the solution for the case where b = 0 (free fall under gravity without friction). Provide rough sketches of the solutions for both cases.