Final answer:
The speed of water pouring out of a 4.0-mm-diameter hole in a bucket filled to a height of 31 cm is approximately 2.47 m/s, as calculated using Torricelli's Law.
Step-by-step explanation:
The question is asking about the speed of water as it leaves a hole in a bucket, and can be calculated based on the principles of fluid dynamics, using Torricelli's Law. This law states that the speed of efflux, v, of water through a hole under the force of gravity can be found by the equation v = √(2gh), where g is the acceleration due to gravity (9.81 m/s2), and h is the height of the water above the hole.
In this case, the height h is 31 cm or 0.31 m. Plugging in the numbers: v = √(2 * 9.81 m/s2 * 0.31 m), we find that the speed v of the water is approximately 2.47 m/s.