Question

2.) 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 10.7 km is moving at 1.7 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

Assuming that the collision is perfectly inelastic ie. the meteor sticks to Earth after the collision. Therefore according to conservation of momentum we can write,

The mass of meteor is,

Here m_m and u_m are mass and initial velocity of meteor respectively, m_e and u_e are mass and initial velocity of earth respectively, v is the final velcocity. Substituting the values we get,

The amount of Kinetic energy lost by the meteor can be calculated as,

No. of Tsar bombs equivalent to this energy is,