I have recently been employed by HMS Nautical Inc to work on their submarine program.I have only some basic data to work with and no idea how to use it to get the information I need.

Here is what I know. First, I know that our Subs have a maximum running depth of 500 feet below sea level.I also know that a sub functioning at acceptable levels should be able to reach maximum depth in 10 minutes.Finally I know that I need to multiply the decent by a factor of 5 to achieve an accurate model.I also have a chart that lists times and depths for the sub.

Time (minutes) Depth in Meters

1 -95

5 -375

9 -495

10 -500

11 -495

15 -375

Finally, I know that the sub follows a quadratic model when it descends and then ascends.

I have been told that you will be able to take this data and make sense of it.I would like a model for the path of the submarine as it descends to its running depth and then returns to the surface.I want to be able to use this model to predict where the sub will be at any time during its decent/ascent cycle.I would also like to know after how many minutes I should expect the sub to breech the surface of the water again.

Please explain clearly how you came up with the model so that I can repeat the process for new additions to our fleet of submarines.I appreciate any help you can give me in this matter.