With a cannon you can’t go much faster than 4-5x the speed of sound, unless the space in between the payload and the explosive is filled with a lighter than air gas like helium. Like in a light gas gun. But even then the acceleration needs to be extremely high since the only thrust the payload gets is at the beginning. So it would destroy most things especially squishy humans. A rail gun would be a better solution and is in theory possible, since it can accelerate the entire length of the rail. If you just make it long enough you can accelerate to any speed in a vacuum at survivable G-forces. But the end of the barrel needs to be in space in a vacuum as well other wise the payload will explode the moment it exists the barrel and hits atmosphere if it’s going fast enough to reach the moon. Though the space craft still needs it’s own thrust system to decelerate, otherwise it will just loop around the moon and fall back to Earth.
With a cannon you can’t go much faster than 4-5x the speed of sound, unless the space in between the payload and the explosive is filled with a lighter than air gas like helium. Like in a light gas gun. But even then the acceleration needs to be extremely high since the only thrust the payload gets is at the beginning. So it would destroy most things especially squishy humans. A rail gun would be a better solution and is in theory possible, since it can accelerate the entire length of the rail. If you just make it long enough you can accelerate to any speed in a vacuum at survivable G-forces. But the end of the barrel needs to be in space in a vacuum as well other wise the payload will explode the moment it exists the barrel and hits atmosphere if it’s going fast enough to reach the moon. Though the space craft still needs it’s own thrust system to decelerate, otherwise it will just loop around the moon and fall back to Earth.