Question

Suppose it takes one minute to fill a 5 gallon bucket with water from your garden hose that is open all the way. the diameter of your hose is 1 inch. how fast is water traveling out of the end of the hose? how fast does it travel if you hold your thumb over the end of the hose and cover half of the area of the hose? (1 inch=0.0254 m, 1 gallon=0.003 78 m3, 1 min=60 s)

Answer 1

The speed of water coming out of the hose can be calculated using the formula v = Q/A. When the diameter of the hose opening is halved, the speed is increased by a factor of 4.

Step-by-step explanation:

The speed of the water coming out of the hose can be calculated using the formula v = Q/A, where v is the speed, Q is the volume flow rate, and A is the cross-sectional area of the hose opening.

To find the volume flow rate, we can convert the volume of the bucket to cubic meters (1 gallon = 0.00378 m^3) and divide it by the time taken to fill the bucket (60 seconds).

When the diameter of the hose opening is halved, the area is reduced by a factor of 4, and therefore the speed is increased by a factor of 4.