Final answer:
The ball will be in the air for approximately 0.39 seconds and will strike the ground 0.156 meters from the edge of the table, calculated using the principles of projectile motion with an initial height of 0.75 meters and a horizontal speed of 0.4 m/s.
Step-by-step explanation:
To calculate the time the ball takes to hit the floor after it rolls off the table and the horizontal distance from the edge of the table to where it strikes the ground, we can use the principles of projectile motion. Here, we ignore air resistance and assume a constant acceleration due to gravity of approximately 9.81 m/s2.
(a) The time it takes for the ball to hit the floor solely depends on the vertical motion and the height from which it falls, which is given as 0.75 meters. Using the formula t = \sqrt{(2h/g)} where h is the height and g is the acceleration due to gravity, we can calculate the time.
t = \sqrt{(2 × 0.75 m) / 9.81 m/s2} = \sqrt{(1.5 m) / 9.81 m/s2} = \sqrt{0.153 m / m/s2} = 0.39 s
(b) To find the horizontal distance, we need the horizontal speed of the ball when it rolls off the edge. Given that the ball travels 0.8 m in 2 s, its speed (v) is 0.4 m/s. It remains constant in horizontal motion as there are no forces acting in that direction (neglecting air resistance). Using the formula x = vt, where x is the distance and t is the time:
x = (0.4 m/s) × (0.39 s) = 0.156 m
Therefore, the ball will be in the air for approximately 0.39 seconds, and it will strike the ground 0.156 meters horizontally from the edge of the table.