When the velocity v of an object is very large, the magnitude of the force due to air resistance is proportional to v with the force acting in opposition to the motion of the object. A shell of mass 2 kg is shot upward from the ground with an initial velocity of 500 m/sec. If the magnitude of the force due to air resistance is (0.1)v, when will the shell reach its maximum height above the ground? What is the maximum height? Assume the acceleration due to gravity to be 9.81 m/s