Final answer:
To fill a 50-liter container with water through a hose having a cross-sectional area of 3 cm² and with water coming out at 25 cm/s, it would take approximately 666.67 seconds.
Step-by-step explanation:
To determine the time required for a 50-liter container to be filled with water, we need to calculate the volume flow rate using the given speed of the incoming water and the cross-sectional area of the hose. The volume flow rate Q can be found with the formula Q = A × v, where A is the cross-sectional area, and v is the speed of the water.
First, we convert the cross-sectional area from cm² to m² to match the SI unit requirements for the flow rate calculation. The cross-sectional area A is 3 cm², which is 3 × 10^-4 m². The speed v is 25 cm/s, which is 0.25 m/s.
Thus, the flow rate Q = 3 × 10^-4 m² × 0.25 m/s = 7.5 × 10^-5 m³/s.
Since the container's volume is 50 liters, we need to convert this to cubic meters to be compatible with the flow rate we just calculated. 50 liters is equivalent to 0.05 m³.
Finally, we find the time t to fill up the container by dividing the container volume by the flow rate:
t = Volume / Flow Rate = 0.05 m³ / (7.5 × 10^-5 m³/s) = 666.67 s
Therefore, it takes approximately 666.67 seconds to fill the 50-liter container with the given conditions.