A raindrop starts falling from the clouds at a considerable height above the surface of the earth. During the fall, the raindrop experiences retardation due to air resistance, which is directly proportional to the instantaneous speed v(t) of the drop.

i) Write the model equations

ii) Is this system static or dynamic? Why?

iii) Obtain an expression for the speed v(t).

iv) Discuss the behaviour of v(t) as the time t changes.

i) The model equations for the motion of the raindrop can be formulated using Newton's Second Law. Let the mass of the raindrop be mm, the gravitational force acting on it be mgmg, and the drag force due to air resistance be kv(t)kv(t), where kk is a constant of proportionality and v(t)v(t) is the speed _______ _______ _________ _______ ________ ________ ______ ________ _____.
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