Why does my windpipe hurt after jogging far?

Likely exertion. Jogging far is a considerable amount of exercise. It might put strain on muscles, your heart, and your lungs. Your windpipe may hurt because your body is trying to get more oxygen into it than when you are resting, even when done jogging. This is to be expected, but if you get difficulty breathing while jogging, see your doctor to test your heart as this may be a sign of heart disease.
Depends. May be hurting from breathing hard through dry airway, especially if breathing hot dry air, but can also be from breathing cold dry air. Possibly asthma-like symptoms.