When the velocity v of an object is very large, the magnitude of the force due to air resistance is proportional to v² with the force acting in opposition to the motion of the object. A shell of mass 4 kg is shot upward from the ground with an initial velocity of 600 m/sec. If the magnitude of the force due to air resistance is (0.1)v², 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/s². dv First write m- -= F(v,t) in terms of the given data. m dv dt

When the velocity v of an object is very large, the magnitude of the force due to air resistance is proportional to v² with the force acting in opposition to the motion of the object. A shell of mass 4 kg is shot upward from the ground with an initial velocity of 600 m/sec. If the magnitude of the force due to air resistance is (0.1)v², 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/s². dv First write m- -= F(v,t) in terms of the given data. m dv dt