If earth had no atmosphere, how would the asteroid's kinetic energy shortly before it impacted the surface compare to its kinetic energy when it was far away from earth? (hint: think about the law of conservation of energy.)

The kinetic energy is the same as in space, which in general is very large

Explanation:

If the Earth had no atmosphere we can use the conservation of kinetic energy in two points

Initial. In space far from the planet

      Em₀ = k = ½ m v₀²

Final. Just before touching the surface of the Earth

      = K = ½ m v²

As there is no rubbing

      Em₀ =

      = ½ m v₀²

The kinetic energy is the same as in space, which in general is very large

When the Earth has an atmosphere we must use the energy work theorem

      W = ΔK

The work is done by the friction forces when the meteor enters the atmosphere, increases in density as it approaches the surface, so the work also increases.

       W = - K₀

        = K₀ - W

        = ½ m v₀² - W

We see that the kinetic energy decreases as the work increases, this makes the impact is higher and part of the meteor also evaporates by friction at the entrance