An asteroid of mass m is approaching earth, initially at a distance 10 R _ e with speed v _ i . It hite oarth with a speed v _ f , ( R _ e and M _ e are radius and mass of earth ) , then

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Correct answer: C. v _f^ 2 = v _i^ 2 + 2G M _ e Rθ (1 - (1)/(10))

Initial energy of the asteroid is E _ i = K _ i + U _ i = (1)/(2)m v _i^ 2 - G M _ θ m 10 R _ e Final energy of the asteroid, E _ f = (1)/(2)m v _f^ 2 - G M _ θ m Rθ According to law of conservation of energy, E _ i = E _ f (1)/(2)m v _i^ 2 - G M _ θ m 10 R _ θ = (1)/(2)m v _f^ 2 - G M _ θ m Rθ v _f^ 2 - 2G M _ θ Rθ = v _i^ 2 - 2G M _ θ 10 R _ θ ⇒ v _f^ 2 = v _i^ 2 + 2G M _ θ Rθ (1 - (1)/(10))

An asteroid of mass m is approaching earth, initially at a distance...

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