a.  Use Newton's Second Law to write a first order differential equation for the velocity of a ball thrown straight upwards at time = 0 sec which then proceeds to fall back down.  Take up to be the positive direction.  The ball experiences a drag force proportional to its velocity:  (Subscript[F, drag]) = -bv, where b > 0.  Take "g" to be inherently positive, putting in any needed signs explicitly.

       b.  Use Mathematica to somehow solve this equation for v(t).  Always use the initial condition v(0) = 10 m/s upwards.  Graph the solution for various representative values of b and m (assume the ball was thrown at a cliff's edge, so it can fall for as much time as needed).  Explain what you see, being as quantitative as you can.  How does your choice of b and m affect your graphs?  Why should we expect this?
       
       
       Be sure to include a printout that shows how you went about telling Mathematica to do these things and a few sample graphs for various b and m values.  Please make it neat.  Alternatively, you may make your printout by hand...meaning you write out the code you used exactly and neatly copy your respresentative graphs.