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Project Orion
Imagine a ship full of nuclear bombs. The ship has a blast shield at its back end. The ship poops out a series of bombs, each of which explode and push the craft forward.
This was a seriously funded research project. They launched functional (non-nuclear) prototypes and penciled out a Mars mission using this technology. The project was thankfully cancelled due to the signing of the 1963 partial nuclear test ban treaty. ~~Because maybe detonating a bunch of nukes in the atmosphere isn't such a good idea, when most of us still need that atmosphere after the rocket is gone.~~
Orion engines weren't ment for atmosphere propulsion
So the other 99% of the energy that doesn't push push against the craft body just goes away? Plus the equal and opposite rule would make it more likely to move the small explosive device away rather than the big heavy rocket away from the device. You set off a bullet outside a gun and the light case moves more than the heavy lead...
I'm no rocket scientist but that sounds like a way to create the least efficient one ever
And you'd be wrong, it is high efficiency and high trust
https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)
You're missing the insane energy density of a nuclear reaction. The first nuke used in war weighed 4700kg and produced about 88 terajoules of energy. That's about 19 giga joule per kilo
1 kg of rocketfuel + oxidizer produces 13 megajoule.
So even at 1% energy conversion for a nuke and 100% conversion for rocketfuel, the nuke is still 15 times more energydense.
And if you don't use nukes from the 40s, a modern thermonuclear bomb packs 2000TJ into 200 kilos, for a convenient 10TJ per kilo, or 7700 times more power per kilo than liquid rocket fuel.
Also the actual propulsive force would have been more like 50%, not 90. So more like almost 400,000x more power per kilo than liquid rocket fuel.
100% Efficiency isn't always the pure aim of rocket engines. As an example, ion engines are the, hands down, most efficient method of powered space propulsion we have in use today. However it would take millions or billions of years for an ion engine to reach near the speed of light. Truthfully it never could because you couldn't carry enough xenon or krypton because of how many years it would take.
Not quite as inefficient as that IIRC, though obviously the core idea was that nuclear bombs are so energy dense that only a fraction of the potential thrust needed to be captured to remain grossly superior to the mass equivalent of any other propellant.