A relatively small impact crater 20 kilometers in diameter could be made by a co

Question

A relatively small impact crater 20 kilometers in diameter could be made by a comet 2 kilometers in diameter traveling at 32 km/s (3.2×104 m/s ).

(A)Assume that the comet has a total mass of 4.2×1012 kilograms. What is its total kinetic energy? (Hint: The kinetic energy is equal to 12mv2, where m is the comet's mass and v is its speed. If you use mass in kilograms and velocity in m/s, the answer for kinetic energy will have units of joules.) Express your answer using two significant figures.

(B)Convert your answer from part A to an equivalent in megatons of TNT, the unit used for nuclear bombs. Comment on the degree of devastation the impact of such a comet could cause if it struck a populated region on Earth. (Hint: One megaton of TNT releases 4.2×1015 joules of energy.) Express your answer using two significant figures.

Explanation / Answer

a )

m = total mass of 4.2 X1012 kilograms

v = 32 km/s = 3.2 X 104 m/s

the Kinetic Energy is KE = 1/2 m v2

KE = 0.5 X 4.2 X1012 X 3.22 X 108

KE = 2.1504 X 1021 J

b)

part A to an equivalent in megatons of TNT is

1 J = 2.39 X 10-10 TNT

and given

One megaton of TNT releases 4.2 X 1015 joules of energy

= 2.1504 X 1021 / 4.2 X 1015

= 512000

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