Answer to Question #126422 in Mechanics | Relativity for Kashish

Question

A 50-kg meteorite moving at 1000 m/s strikes Earth. Assume the velocity is along the line joining Earth's center of mass and the meteor's center of mass. Calculate the amount of kinetic energy converted to internal energy measured from the Earth reference frame. What is the gain in Earth's kinetic energy?

Answer 1

As, mass of the meteorite is very very less compared to mass of earth thus after collision of the meteorite with earth the whole kinetic energy of the meteorite will convert to the potential energy.

Hence, from earth's frame potential energy will be

$$U=mgR$$

Where $R=6400 \:\text{km}$ is the earth's radius.

Thus, $U=313.6\times 10^7J$

Gain in kinetic energy is,

$$T=\frac{1}{2}mu^2\\\implies T=2.5\times 10^7J$$