# Help with Drag Force/Terminal Velocity assignment

Hi, I am a Senior in High school, looking for some help with a couple of questions that deal with both physics and mathematics. I was given a sheet with 4 scenarios on it, I chose a box falling from a height of 5 meters. The information is shown below:

Object mass: 20 grams
Dimensions of box: 15cm x 10cm x 8cm
Times to fall a distance of 5 meters: 1.95, 1.99, 2.03, 1.9, 2.06, 2.12, 2.05, 2.2, 2.07. 1.96

The above are the given data, now my questions include the following:

1) Using the analytic formula, - d(t) = (VT^2 / g)ln[cosh(gt / VT)] - which we will assume to be correct. Determine the terminal velocity (VT).
- The question also states "Solving for VT is difficult, the following method would work more easily: Using a graphing calculator, graph the position function with VT being the unknown, and find when the function is equal to the total distance actually fallen (5m)"

With this question above, can someone please explain what a position function
is and how do I find the function equal to the total distance actually fallen

2) Now we want to find an approximating function for the velocity as a function of time. The area under the velocity time graph should be equal to the distance fallen. You have an estimate for the terminal velocity, but need to approximate the motion by assuming a constant acceleration until the terminal velocity is reached

For this question, I can basically sum it up to this, how do I this? Can someone
also please explain what an approximating function is and how to find it.

The two question above are more of steps that I need to accomplish in order complete the questions that I have, but I am pretty sure I can handle those on my own. Whoever, can answer my questions, Thank you so much.