Final answer:
The water in the hose is moving at a speed of 0.31 m/s.
Step-by-step explanation:
To determine the speed of the water in the hose, we can use the principle of conservation of mass for fluids. The equation that relates the cross-sectional area and velocity of fluid at different points in a pipe is given by A1V1 = A2V2, where A1 and V1 are the cross-sectional area and velocity at the nozzle, and A2 and V2 are the cross-sectional area and velocity in the hose.
First, we need to find the cross-sectional areas at the nozzle and in the hose. The formula for the cross-sectional area of a circle is A = πr², where r is the radius. Therefore, the cross-sectional area at the nozzle (A1) is π(0.001 m)², and the cross-sectional area in the hose (A2) is π(0.00797 m)².
Now, we know the velocity at the nozzle (V1) is given as 25.0 m/s. Using the conservation of mass equation, we can rearrange it to find the velocity in the hose (V2): V2 = (A1/A2) * V1.
Substitute the values into the equation: V2 = (π(0.001 m)² / π(0.00797 m)²) * 25.0 m/s.
After the calculation, we find that V2 is approximately 0.31 m/s.