Model the motion of a body B on a straight line with velocity as given, y(t) being the distance of B from a point y = 0 at time t. Graph a direction field of the model (the ODE). In the field sketch the solution curve satisfying the given initial condition. Two forces act on a parachutist, the attraction by the earth mg (m = mass of person plus equipment, g = 9.8 m/sec² the acceleration of gravity) and the air resistance, assumed to be proportional to the square of the velocity v(t). Using Newton's second law of motion (mass × acceleration = resultant of the forces), set up a model (an ODE for v(t)). Graph a direction field (choosing mand the constant of proportionality equal to 1). Assume that the parachute opens when v = 10 m/sec. Graph the corresponding solution in the field. What is the limiting velocity? Would the parachute still be sufficient if the air resistance were only proportional to v(t)?