The impact of an asteroid
In classical mechanics, linear momentum is the product of an object's mass and velocity. In a closed system (one that does not exchange any matter with the outside world and is not acted on by any outside forces) the total momentum is constant. If a huge asteroid impacts the earth in the same direction as the earth's movement, how will it change the speed of the earth? (Assume that the impact of the asteroid is a perfectly inelastic collision, the mass of the asteroid is
% of the earth's mass, and the speed of the asteroid just before the collision is
times faster than that of the earth.)
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1 solution
As collision is completely inelastic,the asteroid joins the Earth. So from law of conservation of momentum, Mass of asteroid × 10v + Mass of Earth × v = (Mass of Earth + Asteroid) × Unknown velocity 10mv+100mv=101mv' (As mass of asteroid is 1% of mass of Earth) 110v = 101v' Or v'= 110v/101=1.089v=108.9%v So velocity of Earth increases by 8.9%.