A motorboat of total mass m = 200kg is facing the shoreline and drifting away at 0.5 m/s. In order to return to shore you apply a constant force of 100 Newtons in the direction of the shore. However, the boat is also subject to a drag force of 400v2 where v is the velocity in m/s.

(a) Find the ODE satisfied by v( t), the velocity in the direction away from the shore, where t is measured in seconds. (b) Find v(t). (c) How many seconds pass before the boat starts heading toward the shore? (d) What is the interval of existence of the solution? Explain how this is consistent with the Existence and Uniqueness Theorem.