You see him drop the poor girl, and you know you can save her, but how many lives will be lost if you do? There's no time to hesitate, either way. You soar upwards, matching the caped malefactor in speed easily, and wipe the smug look off his face with a single well-placed punch.
He doesn't manage to put up much fight after that, and you're able to turn him over to the police. The police later uncover a giant death ray he had been building, and the press hails you as the savior of untold numbers of lives. You appreciate the fame, but you don't want it. You don't feel like a hero; not when you can see that innocent woman's face every time you close you eyes. When you finally wake from your dream, it's with a deeper understanding of what comes with great power.