Final answer:
To find how long it takes for a ball thrown horizontally at 12 m/s to hit the ground from 3.5 m, we use the formula for time of free fall. The time is about 0.846 seconds.
Step-by-step explanation:
The question at hand involves calculating the time it takes for a ball thrown horizontally at a certain speed to hit the ground, given the height from which it is released. This problem is a classic example of a projectile motion question in Physics, specifically involving free fall.
To calculate the time, we'll apply the formula for the time of free fall, which is derived from the equation of motion under constant acceleration (due to gravity, g = 9.8 m/s2): t = √(2h/g), where h is the height and g is the acceleration due to gravity. Plugging in the height of 3.5 m, the calculation is as follows:
t = √(2 × 3.5 m / 9.8 m/s2)
t = √(7 m / 9.8 m/s2)
t ≈ 0.846 s
Therefore, it would take the ball approximately 0.846 seconds to hit the ground.