The Origin and Physics of the Double Jump
The thing is, no one seems to be sure why it did so. There's never been an explanation. Was it a glitch that the developers decided they liked? Was it a quick fix like I mentioned earlier? Or did the makers of Dragon Buster actually feel like it was a reasonable ability for their hero Clovis to have?
It might have possibly been an intentional variation of an earlier technique that appeared in 1983's Smurf: Rescue in Gargamel's Castle for ColecoVision and Atari 2600. By pressing jump immediately after landing from a previous running jump you enabled your Smurf to jump higher than he previously could. You see the natural evolution of this idea in things like Mario's modern triple jumps. Perhaps Dragon Buster just cut out the landing first part since the initial controls on the arcade cabinet were so difficult to use.
Whatever the origin the impossible ability shows no sign of going anywhere, as evidenced by its presence in the launch title of an eighth generation console... and I don't have an answer to my daughter's question.
I did a little digging around and discovered that a double jump without other means of propulsion is actually possible. You just have to be on Saturn's moon Titan. It is the only satellite in the solar system that contains a sustained atmosphere, and that atmosphere is around 1.45 times as dense as that of the Earth. When you combine that aspect with the moon's low gravity, it should be theoretically possible for a person to "swim" through the air there with a mighty flap of your arms and push of the legs at the top of your jump.
"Knack lives on a moon of Saturn where the air is so thick you can jump off it, sweetie."
Seems as good an explanation as any when you're talking about a magic golem made of colored blocks.