It would if it travelled at the speed of light as "somebody"
suggested. Supersonic is nothing next to superluminal. After all,
what's 360m/s besides 250,000,000m/s?
There are several problems with going at or near light speed:
Firstly, getting to that speed. You can't acceletrate to
250,000km/s in any meaningful amount of time, for the
accelerational forces will quickly turn you to mushroom soup. Even
at an uncomfortable acceleration of 30/s2 or 3gs, it would take you
three months to get to near light speed.
Secondly, you can't really steer at that speed, your path would be
pretty much a straight line, and since you are travelling way
beyond the escape velocity of the earth, you would shoot off in a
straight line into space (and reach the moon in a second) rather
then follow the map of the earth.
Thirdly, there are releativistic time dilation effects to worry
about. (study special relativity)
Fourthly, if you studied energy mass conversion, you would realize
that you cannot exceed the speed of light. Even getting up to near
that speed would require an exponential increase to infinity in
energy required when approaching lightspeed. Short of something
like warp drive, that would mean a complete revolution in modern
physics, you could spend all the energy expended by the human race
on a single hovertank to little purpose.
Fifth, all the projectiles you fire would still travel below the
speed of light, irregardless of even if you are at lightspeed.
(why? study relativity again!)
All in all, even if we did come up with things like deflector
systems and mass dampers, and even warp drive, there is no
meaningful reason why any land unit should be anywhere near
luminial, or superluminal speeds.
And of course, from what you can see, ideas of lightspeed
hovercraft are firmly entrenched in sci-fi, which unfortunately, is
not really science, and useless when we want to predict future
scientific trends, for they are just imaginings. When we predict
the future of war, we go by things we already understand, not pull
something out of the air and say this must be the way.
To this effect, there are working ideas for particle beam weapons,
EM guns, hypersonic smart missiles or even ballistic projectiles.
But non so far for speed of light hovercraft firing laser
projectiles (by the way, lasers are hardly projectiles), and hardly
even any scientific basis for them. We are into intelligent
prediction, not wild conjuncture.