A ball of mass m is dropped from a cliff. As the ball falls, it is subject to air resistance such that the acceleration of the ball a takes the form a=g-bv, where b and g are positive constants and v is the ball speed. The ball eventually reaches a constant value called the terminal speed.
a) What are the MKS units of the quantity b ?
b) Describe qualitatively what happens to the magnitude of the acceleration as the ball falls... does the acceleration increase, decrease, remain the same, decrease then increase, etc.? Please explain clearly.
c) Determine the terminal speed of the ball in terms of parameters of the problem.
d) Determine an expression for the velocity of the ball as a function of time.