Question

The mass of a meteor with a radius of 1 km is about 9 x 1012 kg. The mass of a meteor also is proportional to the cube of its radius. Suppose a meteor with a radius of 8.5 km is moving at 2.0 x 104 m/s when it collides inelastically with the Earth. The Earth has a mass of 5.97 x 1024 kg and assume the Earth is stationary. The kinetic energy lost by the asteroid in this collision will be transferred to non-conservative work in heating the atmosphere and physically destroying the place where it lands. The Tsar Bomb, the largest atomic bomb ever tested, released 2.1 x 1017 J of energy. (Which, by the way, is 1000's of times more energy compared to the atomic bombs dropped in World War II.) How many MILLIONS of equivalent Tsar Bombs is the kinetic energy lost of this meteor?

Answer 1

I am assuming that numbers are written imporperly such as 9 * 1012 kg is 9 * 10¹² kg .

Mass of meteor of radius of 1km is 9 * 10¹² kg.

so, Mass of meteor of radius of 8.5km will be ; m = (9* 10¹²) * 8.5³ =   5.527 * 10¹⁵ kg

Speed of meteor is; v = 2 * 10⁴ m/s

So, kinetic energy of meteor = (1/2) mv²

= (1/2) * 5.527 * 10¹⁵ * (2 * 10⁴)²

= 1.105 * 10²⁴ J

All this kineteic energy will be converterd into Heat

Tsar Atomic Bomb released energy is 2.1 * 10¹⁷ J

So, Ratio of Kinetic energy lost in collision of meteor and energy of TSAR bomb is

(1.105 * 10²⁴ )/( 2.1 * 10¹⁷)

= 5.26 * 10⁶ times or 5.26 Million times