Final answer:
When a ball is thrown vertically downwards towards the ground, the ball undergoes free fall motion. The ball is in the air for 6.0 seconds and its velocity when it lands is -58.8 m/s.
Step-by-step explanation:
When a ball is thrown from an elevated position and free-falls towards the ground, it undergoes projectile motion. In this case, we can consider the vertical motion of the ball.
Using the equation of motion for free fall, we can find the time it takes for the ball to reach the ground. In this case, the time is given as 6.0 seconds. So, the ball is in the air for 6.0 seconds.
Since the ball lands on the ground, its vertical velocity at that moment is 0 m/s. Using the equation for vertical velocity in free fall, we can find the initial vertical velocity, which is also the final vertical velocity when it lands. The equation is: vf = vi + gt, where vf is the final vertical velocity, vi is the initial vertical velocity, g is the acceleration due to gravity (9.8 m/s²), and t is the time. Setting vf = 0 m/s, we can solve for vi to find that the ball's velocity when it lands on the ground is -58.8 m/s (downward direction).