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A relatively small impact crater 20 kilometers in diameter could be made by a comet 2 kilometers in diameter traveling at 25 km/s (2.5×104 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.

Respuesta :

Answer:

[tex]KE=1.3\times 10^{21}\ J[/tex]

[tex]KE=3.1\times 10^{5}\ E[/tex]

Explanation:

(a)

Given:

  • mass of comet, [tex]m=4.2\times 10^{12}\ kg[/tex]
  • velocity of the comet, [tex]v=2.5\times 10^4\ m.s^{-1}[/tex]

Now, the kinetic energy of the comet can be given by:

[tex]KE=\frac{1}{2} m.v^2[/tex]

[tex]KE=0.5\times 4.2\times 10^{12}\times (2.5\times 10^4)^2[/tex]

[tex]KE=1.3\times 10^{21}\ J[/tex]

(b)

Given:

  • energy released by 1 megaton of TNT, [tex]E=4.2\times 10^{15}\ J[/tex]

Now the kinetic energy of the comet in terms of energy of 1 megaton TNT:

[tex]KE=\frac{1.3\times 10^{21}}{4.2\times 10^{15}} E[/tex]

i.e.

[tex]KE=3.1\times 10^{5}\ E[/tex]

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