Question

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.

Answer 1

Answer:

$KE=1.3\times 10^{21}\ J$

$KE=3.1\times 10^{5}\ E$

Explanation:

(a)

Given:

• mass of comet, $m=4.2\times 10^{12}\ kg$

• velocity of the comet, $v=2.5\times 10^4\ m.s^{-1}$

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

$KE=\frac{1}{2} m.v^2$

$KE=0.5\times 4.2\times 10^{12}\times (2.5\times 10^4)^2$

$KE=1.3\times 10^{21}\ J$

(b)

Given:

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

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

$KE=\frac{1.3\times 10^{21}}{4.2\times 10^{15}} E$

i.e.

$KE=3.1\times 10^{5}\ E$