I don't think you quite realize just how much energy we're talking about here. Most asteroids have enough mass, which at a realistic speed could shatter the moon.

If we shatter the moon, well, let's put it this we : at that point we're fucked. As in close to end of human race fucked. There will be worldwide constant meteor showers for years, which will impact with enough force to penetrate nuclear bunkers. Oceans will boil for years.