Final answer:
To find the velocity of the water in the hose, calculate the cross-sectional area and use the volumetric flow rate formula. With a radius of 1cm and a volume flow rate of 1.11*10⁻⁴ m³/s, the velocity can be determined by dividing flow rate by area.
Step-by-step explanation:
To determine the velocity of the water in the hose, you need to use the equation for volumetric flow rate (Q), which is Q = A × v, where A is the cross-sectional area of the hose and v is the velocity of the water. The cross-sectional area A can be calculated using the formula A = π × r², where r is the radius of the hose.
Given that the radius of the hose is 1 cm (or 0.01 m) and the volume flow rate Q is 1.11 × 10⁻⁴ m³/s, the cross-sectional area A of the hose is π × (0.01 m)² = π × (1 × 10⁻⁴ m²). Therefore, the velocity v can be calculated by rearranging the formula to v = Q / A.
Now, plugging in the values gives us v = (1.11 × 10⁻⁴ m³/s) / (π × 1 × 10⁻⁴ m²) = 1.11 × 10⁻⁴ m/s / π × 10⁻⁴ m². By calculating this, we get v which is the velocity of the water in the hose.