Final Answer:
Ball B will hit the ground first.
Step-by-step explanation:
When ball A is rolled off the edge of the table, it has a horizontal velocity, v. This means that it has both a horizontal and a vertical component to its velocity. The horizontal component does not affect the time it takes for the ball to hit the ground, as it is perpendicular to the force of gravity. Therefore, the only factor affecting its time of flight is its initial vertical velocity. On the other hand, ball B is dropped from rest at the same height as ball A. Since it has no initial horizontal velocity, all of its initial velocity is directed vertically downward. As a result, ball B will hit the ground first because it starts with a greater initial vertical velocity than ball A.
In terms of calculations, we can use the equation s = ut + 0.5at^2 to determine the time taken for each ball to hit the ground. Here, s represents the distance fallen, u is the initial vertical velocity, a is acceleration due to gravity (approximately 9.81 m/s^2), and t is time. Since ball A has a non-zero horizontal velocity, we only need to consider its initial vertical velocity when calculating its time of flight. On the other hand, for ball B, we can directly use its initial vertical velocity as u in the equation. By comparing the calculated times for both balls, we can confirm that ball B will indeed hit the ground first.
In conclusion, based on their initial conditions and using basic kinematic equations, we can determine that ball B will reach the ground before ball A due to its greater initial vertical velocity.