There’s two different reasons:
Reason 1 – Size illusion. You know how a jumbo passenger plane looks like it’s going too slow to stay up? Like it should be falling but isn’t? That’s because the length of the plane is huge, so in relative plane-lengths, a fast speed doesn’t look fast. 80 meters per second is one plane-length-per-second in an 80 meter long plane. Larger objects going the same speed as smaller objects appear to be going slower even when going the same speed.
So reason 1: Because the space rocket is longer than an anti-aircraft missile, it would look slower even when going the same speed as it.
Reason 2 – Space rockets have as much fuel as they possibly can, lowering their Thrust to Weight Ratio (TWR). Weapon missiles need to get moving fast on their way to the target, so they don’t pack as much fuel weight as possible as that would slow them down.
Let’s say you have a rocket engine that could push a 100 tonne rocket at a TWR of 3. Three times its weight, meaning after you subtract out the 1G of thrust it would take just to hover, the remaining thrust is still giving you 2G’s upward. It can accelerate up twice as fast as a falling object normally accelerates down. That’s super fast.
So what if you added more fuel to use in that rocket engine? Enough to make the rocket 200 tonnes instead of 100? Well then you now only have a 1.5 TWR. The rocket is heavier so it thrusts up much slower. That’s less efficient… But… what happens after that rocket has burned off 100 tonnes of that fuel? When it’s back to the state the previous version was in with the same engine pushing 100 remaining tonnes?
Then it’s just as good at accelerating as the previous version was, but now it’s starting that state already up in the air, already with some speed going. So it can’t hurt to have added the extra 100 tonnes of fuel. Sure, the 100 additional tonnes are less efficiently used, but once they’re gone you’re back to the same state again, with 100 tonnes left, but now you start in that state after having gotten a bit further along.
It’s always worth it to design more fuel into the rocket even though it will be used inefficiently at first, up to the point where the launch is so slow the rocket doesn’t really work at all. As long as it’s able to accelerate up a *little* when it starts, there’s no harm in the extra fuel weight because that weight will eventually burn away and you’ll be right back to the efficient thrust the lighter version of the rocket with less fuel had on the ground.
Therefore typical space launches have a TWR of about 1.2 to 1.4 off the pad. As long as a quick release isn’t needed to hit a moving target, you may as well have the extra fuel that bogs you down at first.
Also, there is actually some value in a slower launch, since it’s the turning the rocket does in the first 20 seconds of flight or so that really locks in the aim for what the rest of the launch is like, and that turn is easier to accomplish if the rocket isn’t going too fast yet. Once it starts going fast you need to have already been turned down a bit or it will be too hard to forcibly turn it. Momentum and aerodynamics will be forcing it to go straight into the “wind”, and deviating too far from that will induce extra drag and possibly break the rocket walls from the forces pushing sideways on it.
So a low TWR at launch makes it easier to get the aim “dialed in” before the real high speed stuff starts and the rocket’s light shell is too fragile to forcibly turn it into the wind. (unlike a missile where it’s worth it to build it strong so it can course correct at high speed without tearing itself apart.)
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