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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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Detailed Solution

Applying Conservation of Energy, Ui+Ki=Uf+Kf⇒−GMm10R+12m12×1032=−GMmR+12mυf2⇒12mυf2=9GMm10R+12m12×1032⇒υf2=18GM10R+12×1032⇒υf2=9×2GM10R+12×1032⇒υf =9Ve210+12×1032 ⇒υf=911.2×103210+12×1032 Escape Velocity=Ve=2GMR=11.2 km/s⇒υf=112+144×103m/sec ⇒υf=16 km/sec

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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-------