Final answer:
The ball is in the air for approximately 0.71 seconds.
Step-by-step explanation:
To determine the time the ball is in the air, we can use the equation of motion for vertical motion:
h = ut + (1/2)gt^2
Where:
- h is the height of the table (2.5 m)
- u is the initial vertical velocity (0 m/s since the ball is rolling horizontally)
- g is the acceleration due to gravity (-9.8 m/s^2)
- t is the time the ball is in the air (the unknown)
Plugging in the values, we get:
2.5 = 0 + (1/2)(-9.8)t^2
simplifying, we have:
-4.9t^2 = 2.5
t^2 = 2.5/-4.9
t^2 = 0.51
t = √0.51
t ≈ 0.71 seconds
Therefore, the ball is in the air for approximately 0.71 seconds.