Hipersonic rockets travel from 6 to ten times faster than sound. And anti-missile missiles consisting of so-called "missile shields" can shoot down enemy missiles traveling up to three times the speed of sound.
Anti-missile missiles destroy their targets by reaching them and destroying them by hitting them, or by exploding in the immediate vicinity.
And if they are slower than the target, then they can't even shoot him down.
A few days ago, 15.3.2023. The Russians shot down an American drone over the Black Sea with a very interesting tactic. The Russian plane drops some of the fuel in front of the drone, creating an explosive cloud. When the drone flies into such a cloud, the heat of the engine ignites the cloud and it explodes. When the first Russian plane dropped its fuel, the drone managed to avoid the explosive cloud, but when the second Russian plane did the same, the video shows a short-term disappearance of the image, after which the bent propeller on the drone can be seen. After that, the drone began to fall, and the Americans most likely at that moment started the process of erasing all data on the computer controlling the drone, which can be easily achieved with the command to format the disk or memory card.
With this tactic, planes and rockets moving at subsonic speeds could be destroyed. However, rockets that move faster than the explosion of the gas cloud can't be fired by this tactic. If the rocket engine ignites the explosive cloud, the explosion cannot reach the rocket and cannot damage it.
Rockets moving at speeds greater than 6 speeds of sound can only be destroyed in the same way that meteors the size of a grain of rice can damage and destroy rockets and satellites in orbit around the earth.
Such a weapon can be made very easily, by replacing the software in existing anti-missile missiles, and by placing a different missile head. Instead of a lot of explosives, a lot of small lead balls and a little explosive should be placed in the head of the rocket. Such modified rockets would no longer chase the rockets they are supposed to shoot down, but would intercept them by targeting a point that is 7-8 kilometers in front of the rocket they are supposed to shoot down. At the same time, the direction of movement and the speed of both rockets must be calculated well and very quickly. When it reaches the target point, the explosive head should be activated a second before the rocket to be destroyed is found in it, and create a cloud of thousands of small lead shrapnel. In that second, the small shrapnel would spread and create a cloud several hundred meters wide. And then the rocket that needs to be shot down would fly into that cloud of shrapnel. Such small shrapnel would with a very high probability damage the rocket, but would not destroy it immediately. Small shrapnel, thanks to the high speed of the rocket itself, could damage that rocket by hitting the head and the wings that control the rocket. After that, the rocket would continue its uncontrolled movement, making it harmless to its intended target.
And for now, that is the only way hypersonic missiles could be shot down. Other ways will be possible only when anti-missile missiles are made that move at a speed at least ten times faster than sound-
Or by developing much stronger lasers that can pierce the side armor of any missile in a thousandth of a second.
Or the development of magnetic cannons that, placed on planes and ships, fire steel "needles" at a speed at least 20 times faster than sound.