1945, at the end of ww2 the United States dropped two atomic bombs on Japan. But why did they use two different models and not the same type of bomb twice? They obviously knew how construct a functional bomb (after the tests in los alamo), so the reason wasn't testing which one works. My father speculated that one was a bomb that was build by the Nazis, but that is obviously not true. So I want to tell him the real reason why they used different bombs, but I can't find any.
The Manhattan Project, which made the atomic bombs, from the beginning (late 1942) was pursuing two types of nuclear fuel for the bombs: enriched uranium (the production of which involves making massive factories that literally separate individual atoms from other atoms) or plutonium (the production of which involves making and running industrial-sized nuclear reactors). They didn't know which of these approaches would be most successful; both were uncharted territory.
Now they had originally planned to make only one model of bomb, essentially: the "gun type" bomb, where one piece of bomb fuel is shot into another. This is a very simple and conservative bomb design, and their goal was to make the first bombs quickly, so they wanted simple and conservative.
However, in the summer of 1944, they got the first samples of reactor-made plutonium, and they discovered that it had impurities in it that meant it couldn't be used in a gun-type design. It just wouldn't work. (Technically speaking, reactor-made plutonium contains some amount of the isotope plutonium-240, which has a high spontaneous fission rate. This means that it has a lot more neutrons floating around in it than it would otherwise. If you shot one piece of plutonium into another, it wouldn't have a big nuclear explosion — it would "predetonate" too early, and just break itself and make a mess.)
So they had to reorient all of their bomb design work to pursue another kind of bomb, the implosion design. This was much more difficult to pull off than the gun-type design, and involves using specially-made and carefully-detonated high explosives to physically compress a solid sphere of plutonium to about two and a half times its original density.
By sheer coincidence, in July 1945 they ended up with enough highly-enriched uranium for one gun-type bomb, and enough plutonium for two implosion bombs. (I call this a coincidence because the two fuel projects were independent of one another, and their relative setbacks and advances were uncoordinated.) They weren't sure the implosion design would actually work, so they tested it at the Trinity test on July 16. That left them with one uranium bomb, and one plutonium bomb, both using different designs.
The implosion bomb is much more efficient in its use of nuclear material than the gun-type bomb. So could they have taken apart the gun-type bomb and used it to make more implosion bombs? The answer is: yes. This was proposed by J. Robert Oppenheimer right after the Trinity test. The idea was rejected, however, because the Manhattan Project military leaders put the emphasis on time — they wanted to use the atomic bomb as soon as possible, and the scientists estimated it might add several weeks if they did this, and it would require more calculation and careful work to make sure it would also work right.
So at some level, the answer is simply: they happened to have two different bomb types ready to use, and they just used what they had. The reason they had these two designs is because they used two different approaches to nuclear fuel, and it turned out that you couldn't use plutonium with the "easy" approach. They kept the uranium in the "easy" approach because it was already ready to go as such, and they put a high priority on getting it used as soon as possible. So the answer is one part technical (different designs for different fuels), one part political (timing issues), and one part coincidence (them having enough fuel for those bombs at that particular moment).