How will researching what asteroids are made of help us survive on Earth until 2100?

1. For something as difficult as that - you would have six months of warning at least even for a ten kilometer asteroid - smart people know all the ten kilometer asteroids inside of Jupiter's orbit. As we spot hundred kilometer scale objects beyond Neptune's orbit at 30 miles away. List of known objects. If bright, we spot even smaller ones out to that distance.

2. With as little as a few months warning we could make sure that some humans survive in underground and under sea shelters - and we would know which side of the Earth the impact would be because of the news - and which would be the safest places - and could move one side of the world to the other depending on where the asteroids would go(except for a few unwilling or can't be moved).

3. There were big asteroids large enough to erase humanity in the early solar system, and we see their scars on the Moon as the largest craters. But, there are plenty of objects that large in space that are in more stable orbits now and are so far from the sun that there is almost 0% chance of anything like that now.