Final answer:
The velocity of the ball after 4 seconds of free fall from a roof with an acceleration due to gravity of 9.8 m/s^2 is 39.2 m/s directed downwards.
Step-by-step explanation:
The velocity of a ball after falling from the roof with an acceleration of 9.8 m/s2 for 4 seconds can be determined using the formula for the final velocity in uniformly accelerated motion, v = u + at. Since the ball is initially at rest, its initial velocity u is 0 m/s. Thus, the final velocity v after 4 seconds is v = u + at, v = 0 + (9.8 m/s2) (4 s), v 39.2 m/s. Therefore, the velocity of the ball after 4 seconds is 39.2 m/s, directed downwards towards the earth. The downward direction of the velocity aligns with the gravitational pull, confirming the ball's increasing speed under gravity's influence after 4 seconds of free fall.