The year is 1590, and Galileo is standing at the top of the leaning tower of Pisa dropping cannon balls on tourists from Rome. He is laughing is a very disturbing way. The velocity of the ball is v(t), and it obeys the equation dv = g kv(t) . dt In this equation, velocity and distance are measured positive upward. The acceleration due to gravity is g = 9.81 The drag is kv(t). The distance above the ground is s(t) and obeys the equation ds = v(t) . dt The tower is 60 metres high2, and Galileo likes to throw the cannon ball upwards at v = 5, shouting "arrivederci" and laughing in that way he does. (a) Assume that there is no drag, i.e. k = 0. Program a numerical code to integrate the equations. You can, of course, solve them analytically as well. What is the highest point reached by the ball? How long does it take the ball to reach the ground? (b) Now assume a drag of k = 0.4. Repeat the activities above. (c) Assume the drag coefficient is unknown. If the ball reaches the ground in 4.5 seconds, what is k? What is