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

`KE=1.3* 10^(21)\ J`

`KE=3.1* 10^(5)\ E`

Step-by-step explanation:

(a)

Given:

• mass of comet,
  `m=4.2* 10^(12)\ kg`

• velocity of the comet,
  `v=2.5* 10^4\ m.s^(-1)`

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

`KE=(1)/(2) m.v^2`

`KE=0.5* 4.2* 10^(12)* (2.5* 10^4)^2`

`KE=1.3* 10^(21)\ J`

(b)

Given:

• energy released by 1 megaton of TNT,
  `E=4.2* 10^(15)\ J`

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

`KE=(1.3* 10^(21))/(4.2* 10^(15)) E`

i.e.

`KE=3.1* 10^(5)\ E`