Question

A rain drop of initial mass m 0 starts falling from rest under the influence of gra vit y . Assume that the drop gains mass from the cloud at a rate proportional to the pro d uct of its instantaneous mass and its instantaneous v elo cit y:

Answer 1

Answer:

Explanation:

A raindrop with initial mass M0 starts falling from rest under the influence of gravity. Assume that the drop gains mass from the cloud at a rate proportional to the product of its instantaneous mass and velocity:

dM/dt = k M v where k is a constant. Show that the speed of the drop approaches a constant after a long time, derive an expression for the terminal speed, and calculate the terminal speed. Neglect air resistance.

Data: M0 = 0.6 grams; k = 0.06 m^-1.