A ball of mass m is dropped from rest. Let s(t) be the distance that ball traveled after t seconds. Then v(t) = s 0 (t) is the speed and a(t) = v 0 (t) is the acceleration of the ball. We assume that the air resistance is proportional to the speed of the ball. If g is the acceleration due to gravity, then the downward force on the object is mg − cv, where c is a positive constant. The Newton Second Law then gives mv0 = mg − cv.

(1) Solve the above linear differential equation to find the velocity v(t).
(2) What is the limiting velocity of the ball as t → [infinity]?
(3) Find the distance the ball has traveled after t seconds

trig 15.3 cos

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.

i don't understand. explain it clearly