An asteroid is moving directly towards the centre of the earth. When at a distance of $$10R(R$$ is the radius of the $$earth)$$ from the earth’s centre, it has a speed of $$12$$ $$km/s$$. Neglecting the effect of earth’s atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape$$ velocity from the earth is $$11.2$$ $$km/s)? Give your answer to the nearest integer in $$kilometer/s-------$$

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Infinity Learn · Accepted Answer

Applying Conservation of Energy, ​$$Ui+Ki=Uf+Kf$$​⇒−$$GMm10R+12m12$$×$$1032=$$−$$GMmR+12m$$υ$$f2$$⇒$$12m$$υ$$f2=9GMm10R+12m12$$×$$1032$$​⇒υ$$f2=18GM10R+12$$×$$1032$$​⇒υ$$f2=9$$×$$2GM10R+12$$×$$1032$$⇒υf $$=9Ve210+12$$×$$1032$$    ​ ⇒υ$$f=911.2$$×$$103210+12$$×$$1032$$            Escape $$Velocity=Ve=2GMR=11.2$$ $$km/s$$⇒υ$$f=112+144$$×$$103m/$$$$sec$$      ​⇒υ$$f=16$$ $$km/$$$$sec$$

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