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Show at least 10 seconds of the Act 1 video. Ask what questions come to mind. Ask for their best guesses.
Show Act 2 video. You might start by collecting data for only the first four height drops (8 inches down to 6.5 inches). Draw the graph. The sliders initialize with a quadratic coefficient of 0, so you can fit a line to the data. It will fit pretty well at this point.
Next, add a few more data values, at least down to 5 inches, but ideally down to 4. See how well the line fits now. If desired, collect data all the way down to 2 inches, then adjust the quadratic slider to better fit the data.
If you have computers, each student or group can collect their own data and/or find their own model, and they can compare predictions. After you they have used the model to make predictions, show Act 3 to compare the model to reality.
The theoretical basis for this is Torricelli's Law, which states that the rate of flow is proportional to the square root of the water volume. In a rectangular or cylindrical tank, this means the rate of flow is proportional to the square root of the water depth. Solving the corresponding differential equation leads to a theoretical model of h(t) = k(t-c)2 for the water level over time.
This work is licensed under a Creative Commons Attribution 3.0 Unported License