On April 13, 2029 (Friday the 13th!), the asteroid 99942 Apophis will pass within 18600 mi of the earth-about 1/13 the distance to the moon! It has a density of 2600 kg/m^{3}, can be modeled as a sphere 320 m in diameter, and will be traveling at 12.6 km/s.

If, due to a small disturbance in its orbit, the asteroid were to hit the earth, how much kinetic energy would it deliver?
Take the speed of impact with the earth to be

The largest nuclear bomb ever tested by the United States was the "Castle/Bravo" bomb, having a yield of 15 megatons of TNT. (A megaton of TNT releases 4.184 10^{15} J of energy.) How many Castle/Bravo bombs would be equivalent to the energy of Apophis?

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What scientific concept do you need to know in order to solve this problem?

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