top of the line physics problems with minimal prereqs

The following description applies to the union of this post and its companion post with math problems. A few of these are original, many are stolen. There are a few problems here which I independently came up with and later checked that a number of other people had also come up with the problem. The point of the problems is not just to guess the right answer, but to also provide a proof of its correctness (i.e. a compelling argument). A few of the problems are stated a little vaguely, but I think there is a roughly unique way to reasonably resolve the vagueness in each case.

1. You want to be super cool and so on. Your best option for this is to do a bottle flip. For this, your friend has put just the right amount of water into a bottle so that the center of mass of the system consisting of the (upright) bottle and the water in it is as low as possible. Your friend hands you the bottle and a marker. Draw a horizontal line on the side of the bottle which indicates the height of the center of mass of the system.
2. You’re sort of out of shape, so you need to rest for \(10\) seconds somewhere on your way to work. There is an escalator on your way to work. Is it better to rest on the escalator, or a few steps after it?
3. The walk from your home to work is \(10\mathrm{km}\). Your walking speed is \(5\mathrm{km}/\mathrm{h}\). Your dog, however, likes to run at \(10\mathrm{km}/\mathrm{h}\). You and your dog start walking/running from your home, with you just normally walking to work, but with your dog running to your workplace, back to you, to your workplace again, back to you, and so on. What’s the total distance travelled by your dog?