A 1 km wide (.621 mile) asteroid would be enough to cause some SERIOUS problems... that's the guesstimate of the size of the one that killed Dino. The meteor that hit in AZ wasn't a footbal stadium size meteor, that's the size it left.
Meteor crater was left by a 30 - 50 meter wide one.
300 meters could do some serious damage... it would be no 5 mph bumper rub, it would destroy the area the size of a small state. Ocean impacts would produce tsunamis.