Final answer:
The marble fell 41.2 meters under the influence of gravity, taking approximately 2.9 seconds to hit the cup. This was calculated using the free fall equation, which relates the height of fall to the time taken under gravitational acceleration.
Step-by-step explanation:
To determine how long the marble was in the air, we can use the free fall equation for objects in gravitational acceleration without initial vertical velocity, which in physics is given as:
h = (1/2) gt²
Where h is the height (41.2 m), g is the acceleration due to gravity (9.81 m/s² on Earth), and t is the time in seconds. We can solve for t as follows:
41.2 m = (1/2) (9.81 m/s²) t²
t² = (2 * 41.2 m) / (9.81 m/s²)
t² = 8.4 s²
t = √8.4 s²
t ≈ 2.9 s
Hence, the marble was in the air for approximately 2.9 seconds before it fell into the cup.