Question

A rock with 2kg is dropped from 300m with no velocity. As it falls, air resistance is equal to v/8 in pounds where v is the velocity of the ball in feet per second. Find the limiting velocity.

Answer 1

Newton's second law of motion: The net force acting on a body is equal to the time rate of change of the momentum of the body; or, for constant mass,

  

For the problem at hand, there are two forces acting on the body: the force due to gravity given by the weight w of the body, which equals mg, and the force due to air resistance given by -kv, where k > 0 is a constant of proportionality. The minus sign is required because this force opposes the velocity; that is, it acts in the upward, or negative, direction. The net force F on the body is,

When k > 0, the limiting velocity is defined by,