Suppose I put the hat on my hat very loose, then I jump as high as possible, what would happen to my hat?
I think you probably mean "put the hat on my head" since the state of the second hat is not mentioned. If you are jumping, the hat is likely to be pulled off by the air resistance as you begin to fall and slowly fall back later. However, the result can be influenced by the weight and surface area of the hat, as well as how high you can jump. For example, if the hat is almost the same size as your head, it may not experience enough air resistance to slow it down obviously.