The distance a bullet will travel vs the distance it travels with any accuracy are two very different things. Factories considerone mile to be the potential range of the .22 LR for safety purposes. However, its' accurate rangeis limited to shorter distances. Due to its low velocity, the .22 LR has a very steep trajectory, and is very susceptible to wind drift as well. I have heard of matches being fired with .22 LR target rifles at 200 yards, but the groups they produce at such a distance are not particularly small if there is any wind at all.

OTOH, the various HP rilfe rounds you listed can be dangerous out to +-5000 yards if fired at a 30-degree angle of elevation, and the bullet in use is designed for long range, such as the .30 caliber 220-grain Sierra MatchKing. Such a load can be accurate at 1200 yards or more, for target shooting purposes. Even a .243 Win. with a pointed boattail bullet of 100 grains or so could be used at distances up to 600-800 yards for target shooting. I once tried my 22-250 with 55-grain bullets at 500 yards (on a calm day) and was surprised at how well it did on the Army "A" target at that range.

The main factors influencing the distance a bullet can travel are its shape (form factor) and weight in relation to its diameter ("sectional density"). A figure derived from these two factors is called the "ballistic coefficent", a fancy term for a given projectile's ability to overcome air resistance. In addition, the initial speed of the bullet (muzzle velocity)as it leaves the muzzle of the gun has an influence on range as well.

A bullet with good weight in relation to its diameter, witha long, sharp noseon front and a tapered heel on the rear ("boattail") will travel farther than a blunt or round-nosed, stubby one if both start out at the same speed.

If your son is interested in such matters, I suggest he go to the library and ask them to get him a copy of HATCHER'S NOTEBOOK,by Julian S. Hatcher. It has several fascinating chapters on ballistics (and other gun-related subjects).