There is a theory that indicates that dinosaurs became extinct when about 65 mil

Question

There is a theory that indicates that dinosaurs became extinct when about 65 million years ago, a large asteroid hit the Earth surface. Since the energy of impact was high, dust was created in the atmosphere and this dust, caused by this collision, blocked the sunlight reaching the Earths surface and many forms of life became extinct due to the cold. Fearing this threat, how large an asteroid should you be looking for if the dangerous asteroid size is approximately the same as the one that killed the dinosaurs? Available data suggests that about 20 per cent of that asteroids mass ended up as a dust spread evenly over Earth after eventually settling out of the upper atmosphere. About 0.020g/cm2 of dust, which is chemically different than the Earths rock, covered the Earths surface. Typical asteroids have a density of about 2g/cm3. Now that we know the size of the asteroid, how much energy was released during impact, assuming all of it was kinetic?

Possible helpful values: surface area of earth = 5.101x10^14m^2; velocity of asteroid = 20000m/s

Possible formulas: mass = density * volume; mass = area density * area; Although I cannot get these two to give same mass.

Unknown values: radius or diameter; mass; kinetic energy

Please show step by step

Explanation / Answer

Let mass of Asteroid be M

mass of dust m = 20% of m = 0.2M

m = mass density * surface area of earth = 0.020 g/cm2 * 5.101 * 1014 m2 = 0.020 g/cm2 * 5.101 * 1018 cm2 = 1.020 * 1018 g = 1.020 * 1015 kg

M = m/0.2 = 5.1 * 1015 kg

v = 2* 104 m/s

K = 1/2 M v2 = 1/2 * 5.1 * 1015 * 4 * 108 = 1.020 * 1024 J

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