The asteroid which killed the dinosaurs and the majority of the species when it struck was approximately 6 miles wide. The fact that it struck did not immediately kill everything immediately.
The asteroid threw up millions of tons of earth, water and other debris which eventually covered the Earth and cause a nuclear type winter of disaster which blocked the sun and was mainly responsible for destroying the plant-life which fed the animals who eventually died of starvation.
There are 1000s of missiles held in several countries and if all were fired at the same time it would be ample to cause a nuclear winter and radiation poisoning to destroy to world and the vast majority of all lie on the earth including human life..
In fact it would probably take less than 100 missiles to cause a nuclear winter.