3. (10 points) A ball is dropped from rest, and falls in the negative y direction under the force of gravity, together with a drag force +mov,, where a > 0. (a) Use dimensional analysis to find an approximate expression for the terminal velocity of the dropped ball. (b) The velocity of the ball obeys the differential equation dvy - -g+ cuz. dt (2) In units where g = 1 and o = 1, verify that the solution to the differential equation above with the given initial conditions is Uy(t) = - tanh(t). (3)((3) Restore the factors of g and a in the solution above using dimensional analysis. nd the exact expression for the terminal velocity of the ball. ((1) Verify that for small t the solution has the expected forrn mm = -9; + 0(9). (4)