Answer:
They believed that defeating Japan with regular weapons would be too costly in time and lives.
They wanted to be viewed by other nations as the most powerful nation in the world.
Step-by-step explanation:
The U.S. leaders decided to develop atomic weapons as a response to the threat from the Nazis in Germany who were said to have been developing such kinds of weapon. However, under Harry Truman as the President, the U.S. actually dropped the bomb over Japan twice in order to defeat them in a speedy manner. This was also done in order to prevent having many American casualties if they ever invaded.
It is also said that they developed the atomic bomb during the "Cold War." An "arm race" happened whereby nations, especially the U.S. and the Soviet Union, tried to become more superior over the other by developing the best military weapons. When the Soviet tested their atomic bomb, the U.S. also announced that they'd be making an even better atomic bomb. This situation clearly showed how the Americans wanted to be viewed as the most powerful nation in the world.