If the ball was in free fall, there would be only the gravitational force acting on it. Therefore, the ball would move of uniformly accelerated motion, with constant acceleration g, and its velocity at time t would be given by
[tex]v(t) = gt[/tex]
where [tex]g=9.81 m/s^2 [/tex].
Therefore, after t=10 s, its velocity would be
[tex]v(10 s)=(9.81 m/s^2)(10 s)=98.1 m/s[/tex] (a)
However, there is another force acting in the opposite direction: the air resistance. Since the air resistance is proportional to v, its magnitude increases as v increases, up to a point were the air resistance balances the gravitational force. When this occurs, the net force acting on the ball becomes zero, so the acceleration of the ball becomes zero and the velocity remains constant. This represents the maximum velocity of the ball during its motion, and it is called "terminal velocity".
In this problem, the terminal velocity is 21 m/s: this is the maximum velocity the ball can reach during its motion. Therefore, the ball would never reach the speed calculated at point (a). Instead, its velocity after 10 seconds will be 21 m/s.
