Terminal velocity of a falling ball: For objects falling through air, the drag law is not linear but quadratic. A ball of mass m is released from rest and falls through the air under gravity. Air resistance exerts a drag force with magnitude kv2 in a direction opposite to the velocity of the ball, with k being a constant. (a) Write down a force balance on the ball. What is the terminal velocity of the ball? (no need to solve differential equations to answer this) (b) Set up the differential equation for the velocity of the ball as a function of time v(t). Write down the the initial conditions. (c) Solve the differential equation in (b) for v(t). Check that your solution satisfies the initial conditions and approaches the terminal velocity you expect from (a) as t + 0. (Hint: You will need to use a partial fraction decomposition to solve.