Be sure to show all calculations clearly and state your final answers in
complete sentences.
Impact Energies. A relatively small impact crater 20 kilometers in diameter
could be made by a comet 2 kilometers in diameter traveling at 30 kilometers
per second \((30,000 \mathrm{m} / \mathrm{s})\).
a. Assume that the comet has a total mass of \(4.2 \times 10^{12}\) kilograms.
What is its total kinetic energy? (Hint: The kinetic energy is equal to
\(\frac{1}{2} m v^{2}\), where \(m\) is the comet's mass and \(v\) is its speed. If
you use mass in kilograms and velocity in \(\mathrm{m} / \mathrm{s},\) the
answer for kinetic energy will have units of joules.
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 \(4.2 \times 10^{15}\) joules of energy.