Show work please Suppose that and object of constant mass m falls vertically dow

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Show work please

Suppose that and object of constant mass m falls vertically downward under the influence of gravity. If we assume that air resistances is proportional to the speed of the object at any instant during the fail, then according to Newton's second law of motion. F = ma = m(dv/dt), where F is the net force acting on the object in the positive (downward) direction. But F is given by the weight of the object mg (acting downward) minus the air resistance kv (acting upward), where k > 0 is the constant of proportionality, that is, F = mg - kv. Therefore, the equation of motion, with air resistance, is m(dv/dt) = mg - kv A paratrooper and his equipment have a combined with of 192 pounds. At the instant that the parachute is deployed, he is traveling vertically downward at a speed of 30 feet per second. Assume that air resistance is proportional to the instantaneous velocity with constant of proportionality k = 4. Using the previous equation we have a initial value differential equation. 6(dv/dt) = 192 - 4v v(0) = 30 Determine the velocity of the paratrooper at any time. Determine the position of the paratrooper at any time (i.e., the number of feet he has fallen at any time).

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Show work please Suppose that and object of constant mass m falls vertically dow

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