Answer:
If a person begins walking due east, the altitude of Polaris in the night sky would gradually decrease.
Polaris, also known as the North Star, is located very close to the north celestial pole. As a result, it appears to be almost directly overhead for an observer located at the North Pole. For an observer located at any other latitude in the northern hemisphere, the altitude of Polaris above the horizon will be equal to their latitude.
As the person walks due east, they will move away from the north celestial pole, and the angle between their position and the celestial pole will increase. This means that the altitude of Polaris in their night sky will decrease. Eventually, if the person continues walking due east, Polaris will dip below their horizon and they will no longer be able to see it.
It's worth noting that the effect of walking due east on the altitude of Polaris would be relatively small for short distances, as the observer would still be very close to the North Pole. However, for longer distances or for observers at lower latitudes, the effect would be more significant.