Final answer:
The speed of the water in the pipe is approximately 2.85 m/s. This is calculated by using the volume of the bathtub, the time to fill it, and the cross-sectional area of the pipe.
Step-by-step explanation:
To calculate the speed of the water in the pipe, we need to use the volume of the bathtub and the time it takes to fill it. First, we convert the volume from liters to cubic meters (1 L = 0.001 m3), so 500 L is 0.5 m3. Next, we convert the time from minutes to seconds, so 5.5 min is 330 seconds.
Now, we can find the flow rate (volume per unit time) which is 0.5 m3/330 s ≈ 0.001515 m3/s. The flow rate (Q) is also equal to the cross-sectional area (A) of the pipe times the speed (v), Q = A * v. To find A, we use the diameter of the pipe (D = 2.6 cm = 0.026 m) and the formula for the area of a circle, A = π * (D/2)2. This gives us A ≈ π * (0.026/2)2 ≈ 5.3093 * 10-4 m2.
Finally, we solve for the speed, v = Q / A. Substituting the known values, we get v ≈ 0.001515 m3/s / 5.3093 * 10-4 m2 ≈ 2.85 m/s. Therefore, the speed of the water in the pipe is approximately 2.85 m/s.