Elaine went to her outside faucet to fill a 0.0189-m³ bucket with water to wash her car.Water exits with a speed of 0.61 m/s.The radius of the faucet is 0.0078 m.How long does it take to fill the bucket completely?

Question

Quizplus · Accepted Answer

To find the time it takes to fill the bucket, we first calculate the volume flow rate, which is given by the equation $Q = A \cdot v$, where $A$ is the cross-sectional area of the faucet and $v$ is the speed of the water. The area $A$ of the faucet can be calculated using the formula for the area of a circle, $A = \pi r^2$, where $r$ is the radius of the faucet. Substituting the given radius, $0.0078 \, \text{m}$, we get $A = \pi (0.0078)^2 \, \text{m}^2$. The volume flow rate $Q$ then becomes $Q = \pi (0.0078)^2 \cdot 0.61 \, \text{m}^3/\text{s}$.To find the time $t$ it takes to fill the bucket, we use the equation $V = Q \cdot t$, where $V$ is the volume of the bucket. Rearranging for $t$, we get $t = V / Q$. Substituting the given volume of the bucket, $0.0189 \, \text{m}^3$, and the calculated value of $Q$, we can solve for $t$.Plugging in the numbers: $t = 0.0189 / (\pi (0.0078)^2 \cdot 0.61)$, we find that $t \approx 160 \, \text{s}$.

Elaine Went to Her Outside Faucet to Fill a 0