Final answer:
To calculate the speed at which the water leaves a particular fountain, specific details such as height and pressure are required. Instead, an example is provided where the flow rate is calculated for water leaving a faucet with given dimensions and speed.
Step-by-step explanation:
To calculate the speed at which the water leaves the fountain, we need more data specific to that scenario such as the height the water falls from or the pressure behind it. However, we can address a similar example where we are given that water emerges straight down from a faucet with a 1.80-cm diameter at a speed of 0.500 m/s. The formula to calculate the flow rate is Q = A × v, where Q is the flow rate, A is the cross-sectional area of the faucet, and v is the speed of the water.
To find the area, we use the formula for the area of a circle: A = πd²/4. Plugging in the values, A = π(1.8 cm)²/4. The area A is approximately 2.54 cm² when the diameter is 1.80 cm. Now, we can calculate the flow rate by multiplying this area by the speed of 0.500 m/s (which is 50 cm/s when converted to cm/s): Q = 2.54 cm² × 50 cm/s = 127 cm³/s.