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 11.4 km is moving at 1.8 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

First find the mass of 11.4 km radius meteor

Given mass of meteor of radius 1km =9*10¹²kg

and

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Consider the collision

Momentum is conserved

Momentum before collision=Momentum after collision

Mass of meteor is small compared to Earth

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Energy of 1 Tsar Bomb =2.1*10¹⁷ J

No of Tsar Bombs =

No of Tsar Bombs =

No of Tsar Bombs =10028571.43

ANSWER: =10.029 Millions equivalent Tsar Bombs

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