Answer to Question #111397 in Physics for marie

Question

It's not entirely out of this world that an asteroid might strike Earth in the foreseeable future. We have cataloged over 20,000 asteroids that have an orbit close to our planet. Given that about 150 of these near-Earth asteroids are discovered every month, this number will only increase. Imagine an asteroid of mass kg (about the size of a skyscraper) hitting the earth with a speed of 25 km/s. How much energy would be released during this inelastic collision? How does this compare to a 10,000 kiloton of TNT nuclear bomb? 1 kiloton of TNT is J. The mass of earth is

kg.

Answer 1

$$E=0.5\frac{mM}{m+M}v^2$$

$$E=0.5\frac{(78\cdot 10^9)(5.97\cdot 10^{24})}{(78\cdot 10^9)+(5.97\cdot 10^{24})}(25000)^2=24.4\cdot 10^{18}\ J$$

$$\frac{E}{E_0}=\frac{24.4\cdot 10^{18}}{10000\cdot4.184\cdot 10^{12}}=583$$