So specifically I'm looking at three asteroid impacts at once.
Little backstory: It takes place over 100 years in the future. Population steady grew. For unimportant reasons aliens show up. Three separate ships each fire a mass driver on a large urban center. They're fire 'small' asteroids mined beforehand.
They impact Delphi, Shanghai and New York. They need to be large enough the utterly destroy those cities. If the New York one can also destroy DC that would be great. If that would be to big an impact that's fine too.
So I'm looking at the impact on Earth in three time periods. The next few hours/days to deal with the immediate aftermath. Followed by the following weeks/few months. And lastly the story takes place over a century so some long term effects would be nice.
I hope this is concrete enough. So impact on three specific areas, roughly at the same time. Looking at a way that would not utterly annihilate our species.
edit: As the above is to vague I guess we go with each asteroid being about 2km in diameter. They travel about 20km/s. They hit within 30 minutes of each other. They're fired about 150.000km from Earth.
I'm looking at the effects of the impact on the climate of Earth and the how long it should take of the effects to settle. If effects is to vague, severity of the impact winter, temperature drop, earthquakes away from the impact areas.