Question

A large container 116 cm deep is filled with water. If a small hole is punched in its side 89 cm from the top, at what initial speed will the water flow from the hole?

a. Initial speed

b. Container depth

c. Hole distance from the top

d. Container volume

Answer 1

The initial speed of the water flowing from the hole in the container is approximately 2.3 m/s, calculated using Torricelli's law, based on a height difference of 0.27 m.

Step-by-step explanation:

The initial speed at which water will flow from the hole in the container can be determined using Torricelli's law, which states that the speed of efflux under the force of gravity is proportional to the square root of the height difference between the water surface and the hole. Mathematically, the equation is v = √(2gh), where v is the exit velocity, g is the acceleration due to gravity (9.8 m/s²), and h is the height difference. In your case, the container is 116 cm (1.16 m) deep and the hole is 89 cm (0.89 m) from the top, which means the height difference h is 116 cm - 89 cm = 27 cm (0.27 m). Plugging these values into the equation, we get:

v = √(2 x 9.8 m/s² x 0.27 m)

v = √(5.292 m²/s²)

v = 2.3 m/s (approximately)

The initial speed of the water flowing from the hole is approximately 2.3 m/s.